Exhibit 99.1

TEL OFFSHORE TRUST

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

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

TEL OFFSHORE TRUST ANNOUNCES PARTIAL SALE OF ROYALTY INTEREST

AUSTIN, TEXAS OCTOBER 31, 2013—TEL OFFSHORE TRUST (the “Trust”) announced that the TEL Offshore Trust Partnership (the “Partnership”) has consummated a partial sale of the Partnership’s remaining overriding royalty interest in certain oil and gas properties located offshore Louisiana (the “Royalty Properties”).  Upon its formation in 1983, the Partnership received an overriding royalty interest equivalent to a 25% net profit interest in the Royalty Properties.  In 2011, the Partnership consummated a sale of 20% of its overriding royalty interest (or 5% of 8/8ths) and retained 80% of the overriding royalty interest (or 20% of 8/8ths).  On October 31, 2013, the Partnership consummated the sale of 25% of its remaining overriding royalty interest (or 5% of 8/8ths) and following such sale now holds 60% of the overriding royalty interest (or 15% of 8/8ths).  The principal asset of the Trust consists of a 99.99% interest in the Partnership.  In turn, the principal asset of the Partnership is the overriding royalty interest.  The Trust’s source of capital is the Trust’s share of the net proceeds from the Royalty Properties under the terms of the overriding royalty interest held by the Partnership.

The sale was made to RNR Production, Land and Cattle Company, Inc. (“RNR Production”) and closed on October 31, 2013, but was effective as of August 1, 2013 (the “2013 Royalty Sale”).  RNR Production was the purchaser of the partial interest in the overriding royalty interest in 2011 and now holds 40% of the overriding royalty interest (or 10% of 8/8ths).  The 2013 Royalty Sale generated $1,200,000 in gross proceeds and occurred as part of the previously announced formal auction process for the overriding royalty interest.  The Trust expects to receive promptly from the Partnership a distribution of approximately $1,151,885, representing 99.99% of the net proceeds from the 2013 Royalty Sale of $1,152,000.  The Trust intends to use approximately $300,000 of such net proceeds to repay the Trust’s indebtedness under that certain Demand Promissory Note, dated May 23, 2013, in the original principal amount of $300,000, executed by the Trust and payable to The Bank of New York Mellon, N.A., and the remaining net proceeds for the payment of expenses of the Trust.

Chevron U.S.A. Inc. (“Chevron”), as the managing general partner of the Partnership, engaged EnergyNet.com, Inc. to conduct the marketing process and the related open auction for the overriding royalty interest.  EnergyNet.com, Inc. is a FINRA-registered broker dealer that provides marketing services to the oil and gas industry.  Under its engagement agreement, EnergyNet.com, Inc. is entitled to a 4% commission on the $1,200,000 sale price.

As previously disclosed, production from the two most significant Royalty Properties ceased following damage inflicted by Hurricane Ike in September 2008.  The Trust has not received a distribution associated with net proceeds from the overriding royalty interest since December 2008.  Consequently, the Trust has not been able to make a distribution to holders of Trust units since January 9, 2009.  In addition, because of the lack of net proceeds from the overriding royalty interest, the Trust has not had sufficient cash flow to pay its expenses.  As a result and as previously disclosed, the trustees of the Trust provided written notice to Chevron that the Trust needed funds to pay for liabilities of the Trust and the trustees thereby instructed Chevron to effect the sale of the overriding royalty interest as described above.  As stated above, the Trust intends to use the net proceeds from the 2013 Royalty Sale to repay the Trust’s indebtedness to The Bank of New York Mellon, N.A. and for the payment of expenses of the Trust.

This press release contains forward-looking statements.  Although the managing general partner of the 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 of the Royalty Properties alone control historical operating data and handle receipt and payment of funds relating to the Royalty Properties and payments to the Partnership for the related overriding royalty interest.  The Trustees cannot assure that errors or adjustments by such 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 timing of capital expenditures, if any, the actual results of drilling operations, risks inherent in drilling and production of oil and gas properties, the valuation, terms and conditions of any potential sales of the Royalty and Royalty Properties, and other factors described in the Trust’s Form 10-K for 2012 under “Part I, Item 1A. Risk Factors” and in the Trust’s Form 10-Q for the quarterly periods ended March 31, 2013 and June 30, 2013 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.

The Bank of New York Mellon Trust Company, N.A.

AS CORPORATE TRUSTEE

CONTACT:  Mike Ulrich

(800) 852-1422

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