Exhibit 99.1

Alta Mesa Holdings, LP

ALTA MESA ANNOUNCES

FOURTH QUARTER & FULL YEAR 2011

FINANCIAL RESULTS AND OPERATIONAL UPDATE

Houston, Texas – March 27, 2012 – Alta Mesa Holdings, LP announced its financial results for the fourth quarter and full-year of 2011 and provided highlights of its recent operations. A conference call to discuss these results is scheduled for today at 2 p.m. Central time.

Financial and operational highlights of note for 2011 include the following:

“Our financial and operational results for 2011 reflect that we are on track with our strategic goals of consistently and profitably growing EBITDAX and reserves, even in the current low natural gas price environment” stated Alta Mesa’s Chief Executive Officer, Hal Chappelle. “In 2011, we demonstrated our ability to re-direct capital into oil and liquids-rich gas projects within our organic portfolio, and we believe that we have structured our development plan, balance sheet and hedges to enhance profitability in 2012.”

EBITDAX

EBITDAX for the fourth quarter of 2011 was $53.4 million, up $12.7 million, or 31%, compared to $40.7 million for the fourth quarter of 2010. EBITDAX for full-year 2011 was $200.5 million, up $69.3 million, or 53%, compared to $131.2 million for full-year 2010. The increase in EBITDAX between the two annual periods is in large part a result of increased average price realizations, increased production and further movement towards higher margin oil production, all offset in part by increased lease operating expense and general and administrative costs. EBITDAX for the first quarter of 2012 is estimated to range between $50 and $54 million. EBITDAX is expected to continue to grow as Alta Mesa sees the results of a progressive shift of near term capital away from dry-gas projects to higher margin oil and liquids-rich natural gas projects located mainly in Weeks Island, the Eagle Ford Shale, Oklahoma and East Texas.

Production

Production volumes for the fourth quarter of 2011 totaled 10.1 billion cubic feet of gas equivalent (“Bcfe”), or an average of 110 million cubic feet of natural gas equivalent per day (“MMcfe/d”), up 10% compared to 9.4 Bcfe or 102 MMcfe/d for the fourth quarter of 2010. Production volumes for full-year 2011 totaled 41.7 Bcfe, or an average of 114 MMcfe/d, up 10.8 Bcfe, or 35%, compared to 30.7 Bcfe or 84 MMcfe/d for full-year 2010. In addition to new production in Weeks Island and Eagle Ford Shale

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wells, 2011 production was generally higher due to the production increases from the Hilltop field and a full year of production from the assets acquired from Meridian. At the end of 2010, the oil and natural gas liquids portion of Alta Mesa’s production mix was 24%. Since that time, Alta Mesa has made steady and incremental progress in increasing its production levels of higher margin oil and natural gas liquids from within its portfolio of core assets. The percentage of oil and natural gas liquids production was 27% for September 2011, 31% for December 2011 and 33% for February 2012. This level is projected to move to 40% by the end of 2012. Production for the first quarter of 2012 is expected to range between 101 and 105 MMcfe/d.

Realized Revenue & Hedging

Oil and gas revenues for the fourth quarter of 2011 totaled $86.9 million, up $24.0 million, or 38%, compared to oil and gas revenues of $62.9 million for the fourth quarter of 2010. Oil and gas revenues for full-year 2011 totaled $323.9 million, up $115.4 million, or 55%, compared to oil and gas revenues of $208.5 million for full-year 2010. The variance between the two annual periods for oil and gas revenues is due primarily to the increase in oil and natural gas volumes and net change in prices, up 30% for oil and down 7% for natural gas.

In order to maximize the downside price protection and minimize any upside price constraints, Alta Mesa actively manages a portfolio of financial swaps and options and takes positions as far as five years into the future. Realized gains resulting from Alta Mesa’s active management of its hedge portfolio were $8.3 million for the fourth quarter of 2011, and $21.5 million for full-year 2011. The company has over 100% of its expected Proved Developed Producing production hedged for the 2012—2016 time frame at an average floor price of $99.32 per barrel and $4.78 per MMbtu.

Lease Operating Expenses

Total lease operating expenses, inclusive of production taxes, ad valorem taxes and workover expenses, for the fourth quarter of 2011 were $25.5 million compared to $17.6 million for the fourth quarter of 2010. Total lease operating expenses, inclusive of production taxes, ad valorem taxes and workover expenses, for full-year 2011 were $93.8 million compared to $60.5 million for full-year 2010. The increase in lease operating expenses between the two annual periods is due primarily to increased production and the additional costs associated with production from the Meridian acquisition, which occurred in May 2010. Annual workover expense was also up primarily due to activities in Oklahoma, Louisiana and Florida.

General and Administrative Expenses

General and administrative expenses for the fourth quarter of 2011 were $8.8 million compared to $7.2 million for the fourth quarter of 2010. General and administrative expenses for full-year 2011 were $33.1 million compared to $20.1 million for full-year 2010. The increase in general and administrative expenses between the annual periods was primarily the result of increased payroll for additional employees and consulting expenditures, including legal, accounting, tax and compliance services. In addition, general and administrative costs such as office rent, office relocation and system conversions were up compared to 2010.

Net Income

Net income for the fourth quarter of 2011 was $12.4 million, up $47.3 million compared to a net loss of $34.9 million for the fourth quarter of 2010. Net income for full-year 2011 was $65.2 million, up $51.0 million compared to $14.2 million for full-year 2010. The net income between the two annual periods is up primarily due to higher average realized prices and higher production volumes, offset in part by higher lease operating expenses and general and administrative expenses.

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

Operational Highlights

Weeks Island:

The Weeks Island Field, located in Iberia Parish, Louisiana, contains some of Alta Mesa’s largest developed oil reserves. Alta Mesa has continuously employed one drilling rig and one completion rig in this field since mid-2011, resulting in twelve successful oil producing wells in addition to several recompletions. Alta Mesa continues to exploit this historically prolific salt dome oil field, which has over 50 potential pay zones that we believe offer significant opportunities for added production and reserves. Alta Mesa operates all of the wells in this field in which it has a working interest. Additionally, our Weeks Island oil sales contracts are based on the Louisiana Light Sweet crude market price index, which has been consistently higher than the West Texas Intermediate index in 2011.

Eagle Ford Shale:

Alta Mesa’s Eagle Ford Shale assets have grown significantly in terms of oil production and oil reserves. Alta Mesa has between 21% and 25% working interests in 23 producing wells, with approximately 19,000 gross acres in the play. The wells are principally operated by Murphy Oil, which has a 120 well development program in our acreage in the oil and liquids-rich window of the play in Karnes County. Murphy has dedicated up to three drilling rigs, a fracturing team, and a coil tubing unit to the area for the next two years. Alta Mesa also has minor interest in some wells where the acreage it shares with Murphy has been pooled with that of adjacent operators. The crude sold from this field currently receives an average $6 to $10 per barrel premium over the West Texas Intermediate index price. Lease operating costs are improving as much of the temporary infrastructure is now being converted to permanent infrastructure. Net production from this core area has increased by 39% from an average daily production rate in third quarter 2011 of 962 barrels of oil equivalent (“BOE”), to an average daily production rate in the fourth quarter of 1,338 BOE. Production at the end of February 2012 was approximately 1,792 BOE per day, net to Alta Mesa’s interest.

Oklahoma:

Alta Mesa’s assets in Oklahoma are located in large oil fields with multiple pay zones at depths that range from 5,000 feet to 8,000 feet. The fields are located in Kingfisher County, in the Sooner Trend field. These are predominantly long-lived oil fields that were drilled on 80-acre spacing and later waterflooded. Alta Mesa owns working interests in five large units, the Lincoln North Unit (approximately 84%), the Lincoln SE Unit (approximately 89%), the Hennessey Unit (approximately 13%), the East Hennessey Unit (approximately 89%) and the Dover Unit (approximately 28%). Alta Mesa is currently engaged in a low-cost and low-risk program to increase oil production from the Mississippian Lime formation by deepening existing wellbores and evaluating the formation with horizontal drilling. Alta Mesa is also progressively downspacing existing units to 40 acres, as well as commingling oil production in the deeper Mississippian zones through a single tubing string. Capital expenditures for this area are forecasted to jump threefold from last year as Alta Mesa continues to execute its plan to shift its focus to oil and liquids-rich gas projects contained within its asset portfolio. The net combined PV-10 value of these fields at the end of 2011 accounted for approximately 19% of Alta Mesa’s total proved reserves and 34% of its total proved reserves for oil and natural gas liquids.

East Texas Area:

The Hilltop field is one of Alta Mesa’s largest producing assets in terms of volume, with production coming primarily from the Deep Bossier dry gas formation. Due to depressed natural gas prices, capital spending for Deep Bossier gas will be greatly curtailed in 2012. Instead, Alta Mesa will focus on oil and liquids-rich natural gas opportunities in the Woodbine, Eagle Ford and Austin Chalk formations, primarily using horizontal drilling. Currently, Alta Mesa is participating with EnCana in a Woodbine/Eagle Ford drilling program with the initial three wells undergoing completion. Additionally, Alta Mesa recently completed its first operated well in the field, which was a successful horizontal oil well in the Austin Chalk formation. Alta Mesa will continue to pursue opportunities in other prospective

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

and productive formations such as the Buda, Glen Rose, Petet, Woodbine/Eagle Ford and Austin Chalk.

Alta Mesa is continuing to focus on the oil and liquids-rich sands in the Cold Springs area located in San Jacinto County, Texas. Alta Mesa is the largest owner in these fields, with an average 75% working interest in approximately 50 producing wells. Since Alta Mesa took over as operator of the Cold Springs field in mid-2011, it has performed multiple recompletions in the field to prove up a previously untested upper Wilcox section containing about 10 potentially productive shallow oil sands. These shallower Wilcox sands have added meaningful reserves to Alta Mesa’s net interest and are present in numerous other wells in the field which will be further developed with low cost recompletions in the coming months. In 2010 and 2011, Alta Mesa extended Cold Springs with the annex called Cold Springs West, with nine new successful wells targeting liquids-rich prospects in the shallow Yegua formation. The liquids/oil to natural gas makeup of the production in this area is approximately 95 barrels of condensate per million cubic feet of natural gas, which makes these wells economic even in a low natural gas price environment. Additionally, in 2011 seismic data was acquired in the area which identified opportunities for shallow, relatively inexpensive drilling and recompletion activity.

Conference Call Information

Alta Mesa invites you to listen to its conference call which will discuss its financial and operational results at 2:00 p.m., Central time, on Tuesday, March 27, 2012. If you wish to participate in this conference call, dial 877-317-6789 (toll free in US/Canada) or 412-317-6789 (for International calls), five to ten minutes before the scheduled start time and reference Conference ID # 10011542. A webcast of the call and any related materials will be available on Alta Mesa’s website at www.altamesa.net. Additionally, a replay of the conference call will be available for one week following the live broadcast by dialing 877-344-7529 (toll free in US/Canada) or 412-317-0088 (International calls), and referencing Conference ID # 10011542.

Alta Mesa Holdings, LP is a privately held company engaged in onshore oil and natural gas acquisition, exploitation, exploration and production whose focus is to maximize the profitability of our assets in a safe and environmentally sound manner. We seek to maintain a portfolio of lower risk properties in plays where we identify a large inventory of drilling, development, and enhanced recovery and exploitation opportunities in known resources. We maximize the profitability of our assets by focusing on advanced engineering analytics, enhanced geological techniques including 3-D seismic analysis, and proven drilling, stimulation, completion, and production methods. Alta Mesa Holdings, LP is headquartered in Houston, Texas.

Safe Harbor Statement and Disclaimer

This press release includes “forward-looking statements” within the meaning of Section 27A of the Securities Act of 1933, as amended, and Section 21E of the Securities Exchange Act of 1934, as amended. All statements, other than statements of historical fact, regarding Alta Mesa’s strategy, future operations, financial position, estimated revenues and losses, projected costs, prospects, plans and objectives of management are forward-looking statements. When used in this press release, the words “could”, “should”, “will”, “play”, “believe”, “anticipate”, “intend”, “estimate”, “expect”, “project” and similar expressions are intended to identify forward-looking statements, although not all forward-looking statements contain such identifying words. These forward-looking statements are based on Alta Mesa’s current expectations and assumptions about future events and are based on currently available information as to the outcome and timing of future events. These forward-looking statements are based on management’s current belief, based on currently available information, as to the outcome and timing of future events. Forward-looking statements may include statements about Alta Mesa’s: business strategy; reserves; financial strategy, liquidity and capital required for our development program; realized oil and natural gas prices; timing and amount of future production of oil and natural gas; hedging strategy and results; future drilling plans; competition and government regulations; marketing of oil and natural gas; leasehold or business acquisitions; costs of developing our properties; general economic conditions; credit markets; liquidity and access to capital; uncertainty regarding our future operating results; and plans, objectives, expectations and intentions contained in this press release that are not historical. We caution you that these forward-looking statements are subject to all of the risks and uncertainties, most of which are difficult to predict and many of which are beyond our control, incident to the exploration for and development and production of oil and natural gas. These risks include, but are not limited to, commodity price volatility, low prices for oil and/or natural gas, global economic conditions, inflation, lack of availability of drilling and production equipment and services, environmental risks, drilling and other operating risks, regulatory changes, the uncertainty inherent in estimating oil and natural gas reserves and in projecting future rates of production, cash flow and access to capital, the timing of development expenditures, and other risks. Reserve engineering is a process of estimating underground accumulations of oil and natural gas that cannot be measured in an exact way. The accuracy of any reserve estimate depends on the quality of available data, the interpretation of such data and price and cost assumptions made by reservoir engineers. In addition, the results of drilling, testing and production activities may justify revisions of estimates that were made previously. If significant, such revisions would change the schedule of any further production and development drilling. Accordingly, reserve estimates may differ significantly from the quantities of oil and natural gas that are ultimately recovered. Should one or more of the risks or uncertainties described in this press release occur, or should underlying assumptions prove incorrect, our actual results and plans could differ materially from those expressed in any forward-looking statements. All forward-looking statements, expressed or implied, included in this press release are expressly qualified in their entirety by this cautionary statement. This cautionary statement should also be considered in connection with any subsequent written or oral forward-looking statements that we may issue. Except as

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

otherwise required by applicable law, we disclaim duty to update any forward-looking statements, all of which are expressly qualified by the statements in this section, to reflect events or circumstances after the date of this report.

FOR MORE INFORMATION CONTACT: Lance L. Weaver (281) 943-5597 lweaver@altamesa.net

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

ALTA MESA HOLDINGS, LP AND SUBSIDIARIES

CONSOLIDATED STATEMENTS OF OPERATIONS

(unaudited)

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

ALTA MESA HOLDINGS, LP AND SUBSIDIARIES

CONSOLIDATED BALANCE SHEETS

(dollars in thousands)

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

ALTA MESA HOLDINGS, LP AND SUBSIDIARIES

CONSOLIDATED STATEMENT OF CASH FLOWS

(unaudited—dollars in thousands)

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net

GAAP to Non-GAAP Reconciliation

Adjusted EBITDAX is a non-GAAP financial measure and as used herein represents net income before interest expense, exploration expense, depletion, depreciation and amortization, impairment of oil and natural gas, accretion of asset retirement obligations, deferred tax expense, unrealized gain/loss on oil and natural gas derivative contracts and unrealized gain/loss on warrants. We present Adjusted EBITDAX because we believe it is an important supplemental measure of our performance that is frequently used by others in evaluating companies in our industry. Adjusted EBITDAX is not a measurement of our financial performance under GAAP, and should not be considered as an alternative to net income, operating income or any other performance measure derived in accordance with GAAP or as an alternative to net cash provided by operating activities as a measure of our profitability or liquidity. Adjusted EBITDAX has significant limitations, including that it does not reflect our cash requirements for capital expenditures, contractual commitments, working capital or debt service. In addition, other companies may calculate Adjusted EBITDAX differently than we do, limiting its usefulness as a comparative measure.

The following table sets forth a reconciliation of net income (loss) as determined in accordance with GAAP to Adjusted EBITDAX for the periods indicated:

15021 Katy Freeway, Suite 400     Ÿ    Houston, Texas 77094    Ÿ     (281) 530-0991    Ÿ     www.altamesa.net