Exhibit 99.1

MURPHY OIL ANNOUNCES FIRST QUARTER 2010 EARNINGS

AND RESULTS OF DRILLING WELLS

EL DORADO, Arkansas, May 5, 2010 – Murphy Oil Corporation (NYSE: MUR) announced today that net income in the first quarter of 2010 was $148.9 million ($0.77 per diluted share), compared to net income of $171.1 million ($0.89 per diluted share) in the first quarter of 2009. The 2010 quarterly results included net after-tax losses of $41.3 million ($0.21 per diluted share) on transactions denominated in foreign currencies, while the 2009 results included after-tax gains of $26.1 million ($0.14 per diluted share) on these transactions. Net income in 2009 included income from discontinued operations of $99.9 million ($0.52 per diluted share) associated with Ecuador operations that were sold at a preliminary after-tax gain of $104.0 million in March 2009. Income from continuing operations for the three months ended March 31, 2010 and 2009 was $148.9 million ($0.77 per diluted share) and $71.2 million ($0.37 per diluted share), respectively.

The 109% improvement of income from continuing operations in 2010 compared to 2009 was primarily due to a 50% higher average realized crude oil sales price, which led to significantly higher earnings in the Company’s exploration and production business. Operating results for the Company’s refining and marketing business in the 2010 first quarter were significantly weaker than the prior year due to lower refining margins in the current period and planned shutdowns for major turnarounds at the Company’s two largest refineries at Meraux, Louisiana and Milford Haven, Wales. The turnarounds reduced production of refined products, and therefore, corresponding products sales volumes. The net cost of Corporate activities was $68.4 million in the 2010 quarter compared to a net benefit of $10.1 million in the prior year’s quarter. The unfavorable 2010 Corporate variance was primarily caused by significant losses on transactions denominated in foreign currencies in 2010, while 2009 included benefits from these foreign currency transactions.

Exploration and Production (E&P)

Murphy’s income contribution from continuing E&P operations was $247.0 million in the first quarter of 2010 compared to $50.3 million in the same quarter of 2009. Higher realized sales prices for crude oil were the primary driver for the improvement, but the current period also benefited from higher natural gas sales volumes, higher natural gas sales prices and lower exploration expenses compared to 2009.

The Company’s worldwide crude oil, condensate and natural gas liquid sales prices averaged $64.89 per barrel for the 2010 first quarter compared to $43.15 per barrel in the 2009 first quarter. Total crude oil, condensate and gas liquids production of 139,060 barrels per day in the first quarter of 2010 was slightly below the 139,318 barrels per day produced in the 2009 quarter. Excluding production in 2009 from discontinued operations in Ecuador, which the Company sold in the first quarter 2009, quarterly oil production increased 4% in 2010. The increase in oil production volumes from continuing operations in 2010 was mostly attributable to production that started up in the third quarter 2009 at the Thunder Hawk field in the Gulf of Mexico and the Azurite field, offshore Republic of the Congo. Despite higher oil production from continuing operations in 2010, net oil production volumes declined at several areas in the current period. Heavy oil production in Western Canada declined primarily due to a higher royalty rate resulting from project payout and higher net profits at properties in the Seal area. Net oil production volumes were also lower offshore Eastern Canada where the Terra Nova field experienced production decline and Hibernia and Terra Nova had higher net profits royalty rates. Synthetic net oil production at Syncrude in Alberta was lower in 2010 primarily due to a higher net profits royalty rate. Oil production declined in Malaysia in the 2010 quarter compared to 2009 due to a lower percentage of the Kikeh field’s gross production being allocable to the Company under the production sharing contract. But this impact was somewhat offset in Malaysia by new condensate volumes associated with a natural gas field offshore Sarawak. Total sales volumes of crude oil, condensate and natural gas liquids from continuing operations averaged 145,783 barrels per day in the first quarter 2010 compared to 129,595 barrels per day in the 2009 quarter. Oil sales volumes exceeded oil production volumes in the 2010 first quarter primarily at the Kikeh field due to the timing of periodic large oil tanker sales. North American natural gas sales prices averaged $5.14 per thousand cubic feet (MCF) in the 2010 first quarter compared to $4.66 per MCF in the same quarter of 2009. Natural gas sales volumes were a quarterly record for the Company of 343 million cubic feet per day in the first quarter of 2010 compared to 111 million cubic feet per day in the 2009 period. The more than 200% increase in natural gas sales volumes was due to continued ramp-up of natural gas production at the Tupper field in British Columbia, the third quarter 2009 start-up of natural gas production offshore Sarawak Malaysia and at Thunder Hawk in the Gulf of Mexico, and higher natural gas sales volumes at the Kikeh field offshore Sabah due to more uptime at the onshore processing plant owned by a third party.

Exploration expense in the 2010 period was $66.3 million compared to $111.1 million in 2009. Dry hole expense was lower by $45.2 million in the 2010 period mostly due to

unsuccessful drilling offshore Western Australia in 2009. Geological and geophysical expense was $2.2 million higher in 2010 compared to 2009 due to more seismic work in the Gulf of Mexico, but mostly offset by significant spending in the 2009 quarter for 3-D seismic covering offshore Block 37 in Suriname. Undeveloped leasehold amortization expense in 2010 was $4.9 million less than in 2009 as lower amortization costs for the Tupper area in Western Canada were somewhat offset by higher costs for leases in the Eagle Ford shale area of South Texas.

Refining and Marketing (R&M)

Murphy’s R&M operations had a loss of $29.7 million in the 2010 first quarter compared to income of $10.8 million in the 2009 quarter. In the United States, R&M operations lost $14.7 million in 2010 compared to earnings of $14.6 million in 2009. U.S. manufacturing operations reflected a loss of $23.6 million in the 2010 quarter, a decrease of $31.9 million compared to the first quarter 2009. Very weak refining margins were caused by higher prices for crude oil feedstocks and shutdown of the Meraux, Louisiana refinery for a planned turnaround for approximately six weeks during the 2010 quarter. U.S. marketing operations posted a profit of $8.9 million in the 2010 quarter, an increase of $2.6 million compared to the same quarter in 2009, as margins for U.S. retail marketing operations were stronger in the 2010 quarter compared to a year earlier. Refining and marketing operations in the United Kingdom incurred a loss of $15.0 million in the first quarter 2010 compared to a loss of $3.8 million in the same quarter of 2009, with the decline primarily due to a combination of weaker refining results in the most recent quarter and downtime associated with a turnaround at the Milford Haven, Wales, refinery during a portion of the 2010 quarter.

Corporate

Corporate functions had net costs of $68.4 million in the 2010 first quarter compared to a net benefit of $10.1 million in the 2009 first quarter. The significant unfavorable variance in 2010 was due to after-tax losses of $41.3 million in 2010 on transactions denominated in foreign currencies compared to after-tax gains of $26.1 million in 2009. The charges in 2010 were generated due to a combination of a stronger U.S. dollar versus the British pound and a weaker dollar versus the Malaysian ringgit. The stronger U.S. dollar led to foreign currency losses on dollar based liabilities in the sterling functional U.K. downstream operations, and the stronger Malaysian ringgit led to foreign currency losses on ringgit based income tax liabilities in the dollar functional Malaysian oil and gas operations. The 2009 quarter benefited from a stronger U.S. dollar compared to the Malaysian ringgit, which led to foreign currency gains on Malaysian

income tax liabilities. The Company had higher net interest expense in 2010 than in 2009 due to a combination of higher average borrowings and a smaller portion of interest capitalized to ongoing oil and natural gas development projects in 2010.

Exploration Activities

Murphy also announces successful well results at DC4 in the Gulf of Mexico, at the Dolfin prospect, offshore Sabah, Malaysia, and in the Eagle Ford shale, onshore Texas.

In the Gulf of Mexico, the DC4 well in De Soto Canyon was drilled to a total depth of 13,195 feet and encountered 156 feet of oil pay in three zones. Murphy is the operator of DC4 with a working interest of 64.2%.

The Dolfin well drilled in Block H, offshore Sabah, Malaysia, found 33 feet of natural gas pay. The Batai well, also drilled offshore Block H, found noncommercial quantities of hydrocarbons and has been plugged and abandoned. Murphy is operator of the Dolfin and Batai wells and has a 60% working interest along with PETRONAS Carigali, with a 40% interest.

In the Eagle Ford shale play in South Texas, the Drees A-79 1-H well in Karnes County was drilled to a measured depth of 17,340 feet and following a 15-stage fracture treatment along a lateral section of 4,985 feet, flowed at initial rates of 1,462 barrels of oil per day and 1.25 million cubic feet of gas per day. The Company currently has two rigs drilling in the trend, where Murphy has accumulated over 200,000 net acres. Murphy has a 100% working interest in the Drees well.

David Wood, Murphy’s President and Chief Executive Officer, commented, “This is an active exploration year for us and it is off to a good start, with bigger targets ahead. In Block H, we continue to prove up additional natural gas volumes across the block and are studying development options. The DC4 well, offsetting last year’s natural gas discovery at Dalmatian, shows oil upside in that block that may hold additional prospective potential. The onshore Drees well had a 30-day production average of 1,264 barrels of oil and 1.1 million cubic feet of gas per day–clearly a strong result. Our focus is on appraising and ultimately developing this part of our Eagle Ford acreage as we continue to assess our other holdings across the play.

“In downstream, our construction team continues the expansion of the retail marketing network with about 20 new builds in progress. In the U.K. the Milford Haven refinery continues its planned turnaround and should be running in early May. We are using the associated downtime to complete the upgrade of the facility as the plant will come out of the turnaround with the capability to run 130,000 barrels of crude oil per day, up from the present 108,000 barrel per day capacity.

“We anticipate total worldwide production volumes of about 188,000 barrels of oil equivalent per day is in the second quarter of 2010. Production volumes are projected to be lower in the second quarter 2010 than in the first quarter primarily in Malaysia due to a mechanical issue at a third party operated LNG facility that will reduce Sarawak gas sales and due to well intervention work on a subsea oil producing well that will reduce oil production at the Kikeh field. Sales volumes of oil and natural gas are projected to average 184,000 barrels of oil equivalent per day in the second quarter 2010. We anticipate full year 2010 production volumes of 200,000 barrels of oil equivalent per day. At the current time, we expect consolidated earnings in the second quarter to range between $1.15 and $1.25 per diluted share. Exploration expense should total between $60 million and $90 million during the quarter. The estimate includes projected earnings from our downstream businesses of approximately $28 million. Results could vary based on commodity prices, drilling results and timing of crude oil and natural gas sales, refining and marketing margins, and foreign exchange movements.”

The public is invited to access the Company’s conference call to discuss first quarter 2010 results on Thursday, May 6, at 12:00 p.m. CDT either via the Internet through the Investor Relations section of Murphy’s website at http://www.murphyoilcorp.com/ir or via the telephone by dialing 1-877-941-2927. The telephone reservation number for the call is 4281227. Replays of the call will be available through the same address on the Murphy website, and a recording of the call will be available through May 10 by dialing 1-800-406-7325. Audio downloads will be available on the Murphy website through June 1 and via Thomson StreetEvents for their service subscribers.

Summary financial data and operating statistics for the first quarter 2010 with comparisons to 2009 are contained in the attached tables.

This press release contains forward-looking statements as defined in the Private Securities Litigation Reform Act of 1995. These statements, which express management’s current views concerning future events or results, are subject to inherent risks and uncertainties. Factors that could cause actual results to differ materially from those expressed or implied in our forward-looking statements include, but are not limited to, the volatility and level of crude oil and natural gas prices, the level and success rate of our exploration programs, our ability to maintain production rates and replace reserves, political and regulatory instability, and uncontrollable natural hazards. For further discussion of risk factors, see Murphy’s 2009 Annual Report on Form 10-K on file with the U.S. Securities and Exchange Commission. Murphy undertakes no duty to publicly update or revise any forward-looking statements.

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MURPHY OIL CORPORATION

FUNCTIONAL RESULTS OF OPERATIONS (Unaudited)

(Millions of dollars)

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OIL AND GAS OPERATING RESULTS (Unaudited)

THREE MONTHS ENDED MARCH 31, 2010 AND 2009

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SUMMARIZED CONSOLIDATED STATEMENTS OF INCOME (Unaudited)

(Thousands of dollars, except per share amounts)

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SUMMARIZED CONSOLIDATED STATEMENTS OF CASH FLOWS (Unaudited)

(Thousands of dollars)

MURPHY OIL CORPORATION

OTHER FINANCIAL DATA

(Unaudited, except for December 31, 2009)

(Millions of dollars)

MURPHY OIL CORPORATION

STATISTICAL SUMMARY

MURPHY OIL CORPORATION

STATISTICAL SUMMARY (Continued)