Exhibit 99.1

Individual Trustees

Gary C. Evans

Thomas H. Owen, Jr.

Jeffrey S. Swanson

TEL OFFSHORE TRUST

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., CORPORATE TRUSTEE

919 CONGRESS AVENUE / (800) 852-1422 / AUSTIN, TEXAS 78701

TEL OFFSHORE TRUST ANNOUNCES THERE WILL BE NO FIRST QUARTER 2011 DISTRIBUTION

AUSTIN, TEXAS MARCH 30, 2011—TEL OFFSHORE TRUST announced that there will be no trust distribution for the first quarter of 2011 for unitholders of record on March 31, 2011. The Trust has not been able to make a distribution to unitholders for nine consecutive quarters, or since January 9, 2009. The financial and operating information included herein for the Trust’s first quarter of 2011 reflects financial and operating information with respect to the royalty properties for the months of November and December 2010 and January 2011.

Gas revenues recorded by the Working Interest Owners on the royalty properties decreased approximately 61% to $168,351 in the first quarter of 2011 from $434,071 in the fourth quarter of 2010.  Natural gas volumes during the first quarter of 2011 decreased approximately 50% to 42,427 Mcf from 84,237 Mcf during the fourth quarter of 2010. The decrease in volumes is due primarily to the shut-in of the platform at Ship Shoal 182/183 during November 2010 for a tank replacement. The average price received for natural gas decreased approximately 23% to $3.97 per Mcf in the first quarter of 2011 as compared to $5.15 per Mcf received in the fourth quarter of 2010.

Crude oil revenues recorded by the Working Interest Owners on the royalty properties decreased approximately 21% to $2,807,095 in the first quarter of 2011 from $3,553,883 in the fourth quarter of 2010. Oil volumes during the first quarter of 2011 decreased approximately 28% to 32,520 barrels, compared to 45,399 barrels of oil produced in the fourth quarter of 2010. The decrease in volumes is due primarily to the shut-in of the platform at Ship Shoal 182/183 during November 2010 for a tank replacement. The average price received for oil increased approximately 10% to $86.32 per barrel in the first quarter of 2011 as compared to $78.28 per barrel received in the fourth quarter of 2010.

The Trust’s share of capital expenditures decreased by $552,725 in the first quarter of 2011 to $562,505, as compared to $1,115,229 in the fourth quarter of 2010.  The higher capital expenditures in the fourth quarter of 2010 relate primarily to an oil and sump tank upgrade at Ship Shoal 182/183. The Trust’s share of operating expenses decreased by $4,846,285 in the first quarter of 2011 to $3,713,384 as compared to $8,559,670 for the fourth quarter of 2010. The decrease in operating expenses is due primarily to less well and platform abandonment work being conducted at Eugene Island 339.

For the first quarter of 2011, under the terms of the conveyance for the royalty properties, production costs for the royalty properties exceeded gross proceeds thereof, with the Trust’s portion of such excess equal to approximately $380,000. As of January 31, 2011, aggregate development and production costs for the royalty properties since November 2008 have exceeded the related proceeds of production from the royalty properties by approximately $3.5 million, after taking into account insurance proceeds received by Chevron U.S.A., Inc. and allocated to Eugene Island 339, net to the royalty interest.  As a result, the Trust will not be receiving any net proceeds for the first quarter of 2011.  In the fourth quarter of 2010, Chevron

U.S.A., Inc. withdrew $4,304,894 from the Special Cost Escrow account of the Working Interest Owners (a reserve fund for certain costs) to cover expenses incurred in connection with the plugging and abandonment of Eugene Island 339, which served to reduce the amount by which development and production costs exceeded the related proceeds from production; however, additional deposits to the Special Cost Escrow account will be required in future periods in accordance with the terms of the underlying conveyance of the royalty if, and when, net proceeds would otherwise be payable on the royalty.  In the first quarter of 2011, no dollars were escrowed or released from the Special Cost Escrow account of the Working Interest Owners, leaving a balance of $1,000 in the Special Cost Escrow account.

This press release contains forward-looking statements.  Although the Managing General Partner of the TEL Offshore Trust Partnership has advised the Trust that the Managing General Partner believes that the expectations contained in this press release are reasonable, no assurances can be given that such expectations will prove to be correct. The Working Interest Owners alone control historical operating data, and handle receipt and payment of funds relating to the royalty properties and payments to the Trust for the related royalty. The Trustees of the Trust cannot assure that errors or adjustments by the Working Interest Owners, whether historical or future, will not affect future royalty income and distributions by the Trust.  Other important factors that could cause these statements to differ materially include delays and costs in connection with repairs or replacements of hurricane-damaged facilities and pipelines, including third-party transportation systems, the actual results of drilling operations, risks inherent in drilling and production of oil and gas properties, and other factors described in the Trust’s Form 10-K for 2009 under “Item 1A. Risk Factors” and in the Trust’s Form 10-Q for the quarterly period ended September 30, 2010 under “Part II, Item 1A. Risk Factors”.  Statements made in this press release are qualified by the cautionary statements made in these risk factors. The Trust does not intend, and assumes no obligations, to update any of the statements included in this press release.

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