Exhibit 99.1

TEL OFFSHORE TRUST

THE BANK OF NEW YORK MELLON TRUST COMPANY, N.A., CORPORATE TRUSTEE 919 CONGRESS AVENUE / (512) 236-6599 / AUSTIN, TEXAS 78701

TEL OFFSHORE TRUST PROVIDES UPDATE ON PROBATE PROCEEDING AND ANNOUNCES THERE WILL BE NO THIRD QUARTER 2014 DISTRIBUTION

AUSTIN, TEXAS October 6, 2014—TEL OFFSHORE TRUST (the “Trust”) provided an update on the previously announced probate proceeding and also reported that there will be no trust distribution for the third quarter of 2014.

Update on Probate Proceeding

As previously disclosed by the Trust, The Bank of New York Mellon Trust Company, N.A., as Corporate Trustee, and Gary C. Evans, Jeffrey S. Swanson and Thomas H. Owen, Jr., as Individual Trustees (collectively, the “Trustees”), filed a Petition for Modification and Termination of Trust (the “Petition”) with the Probate Court of Travis County, Texas (the “Court”), in Cause No. C-1-PB-14-001245 (the “Probate Proceeding”).  The Petition requests the Court to modify the TEL Offshore Trust Agreement (the “Trust Agreement”) to (1) allow for the termination of the Trust by a court order, and (2) allow the Trustees, as necessary to fulfill the purposes of the Trust and, without the approval of the Trust’s unitholders, to (a) sell all or any portion of the Trust’s interest in the TEL Offshore Partnership (the “Partnership”) or any other assets of the Trust, (b) exercise their rights to dissolve the Partnership, or (c) cause the Partnership to sell the remaining overriding royalty interest owned by the Partnership.  The goals in filing the Probate Proceeding are to permit the Trustees to direct the Partnership to sell the remaining overriding royalty interest held by the Partnership; to distribute the net proceeds, if any, resulting from such sale, after the payment of the Trust’s liabilities and expenses, to the Trust’s unitholders; and, to thereafter terminate the Partnership and the Trust.  There can be no assurances whether the Court will grant the requested relief, and if such relief is granted, when such actions will be completed.  In addition, if the Court does grant the requested relief, there can be no assurance as to the amount, if any, of the net proceeds that will be available for distribution to the Trust’s unitholders.

The Trust is in the process of serving the Petition on the Trust’s unitholders and it is expected that this process will continue for several weeks.  The Trust and the Trustees wish to confirm that they are not seeking a finding of any liability against any of the Trust’s unitholders in the Probate Proceeding and that they are not seeking any money or damages from any of the Trust’s unitholders.  Under Texas law, the beneficiaries of the Trust are necessary parties to the Probate Proceeding and, therefore, the Trustees are required to serve the Petition on the Trust’s unitholders.  It is not the purpose of the Probate Proceeding to seek any recovery from the Trust’s unitholders, and the Trustees will not seek a judgment against the Trust’s unitholders.

The Trust will continue to provide information regarding the status of the Probate Proceeding in its filings with the Securities and Exchange Commission (“SEC”) and, to the extent appropriate, will issue press releases providing additional information regarding the Probate Proceeding. All documents that are filed in the Probate Proceeding and all of the Trust’s future filings with the SEC during the Probate Proceedings can be viewed at: www.andrewskurth.com/teloffshoretrust.

Third Quarter 2014

The Trust will not make a distribution for the third quarter of 2014 to unitholders of record on September 30, 2014.  The Trust has not been able to make a distribution to unitholders for twenty-three consecutive quarters, or since January 9, 2009. Except as disclosed below, the financial and operating information included herein for the Trust’s third quarter of 2014 reflects financial and operating information with respect to the royalty properties for the months of May, June and July 2014.

Gross proceeds for the burdened royalty properties exceeded development and production costs for the months of May, June and July 2014 by $2,733,945, or $683,486 net to the entire overriding royalty interest, and $410,092 attributable to the Trust.  The excess proceeds, net to the entire overriding royalty interest, were applied to reduce the accumulated excess cost carryforward, which represents the amount by which the aggregate development and production costs for the burdened royalty properties since November 2008 have exceeded the related proceeds of the production.

Gas revenues recorded by Chevron USA, Inc. (“Chevron”), the Managing General Partner of the TEL Offshore Trust Partnership (the “Partnership”) for the quarter on the burdened royalty properties increased approximately 20% to $351,077 from $292,564 in the second quarter of 2014. Natural gas volumes during the third quarter of 2014 increased approximately 29% to 73,562 Mcf from 57,233 Mcf during the second quarter of 2014. The increase in production is primarily due to wells coming back on line after maintenance work was performed at Ship Shoal 182. Excluding the impact of prior period adjustments, the average price received for natural gas production decreased approximately 7% to $4.82 per Mcf in the third quarter of 2014 from $5.16 per Mcf in the second quarter of 2014.

Crude oil and condensate revenues recorded by Chevron for the quarter on the burdened royalty properties increased approximately 6% to $3,689,442 in the third quarter of 2014 from $3,470,334 in the second quarter of 2014.  Crude oil and condensate volumes during the third quarter of 2014 increased approximately 6% to 35,777 barrels, compared to 33,858 barrels during the second quarter of 2014.  The increase in production is primarily due to wells coming back on line after maintenance work was performed at Ship Shoal 182.  Excluding the impact of prior period adjustments, the average price received for crude oil and condensate production increased approximately 1% to $103.13 per barrel in the third quarter of 2014 from $102.52 per barrel in the second quarter of 2014.

Capital expenditures increased by approximately 13%, or $2,087, to $18,031 in the third quarter of 2014 from $15,943 in the second quarter of 2014. Operating expenses decreased by approximately 14%, or $195,177, to $1,172,305 in the third quarter of 2014 from $1,367,482 in the second quarter of 2014.

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As previously disclosed, during September 2008, the platforms, wells and infrastructure associated with the Eugene Island 339 field were completely destroyed by Hurricane Ike.  While Chevron has completed the work it deemed required to clear the remaining infrastructure and abandon those wells, platforms and infrastructure, the interruption in production and the plugging and abandonment costs, each related to the Eugene Island 339 field, were the primary contributors to the resulting excess of development and production costs over proceeds of production.  Chevron has informed the Trust that the estimate of the Trust’s net portion of the aggregate cost to plug and abandon the wells, remove and abandon platforms and infrastructure and remediate the surface subject to the overriding royalty interest on Eugene Island 339 was approximately $19.8 million.  No further expenses are expected to be incurred.

As discussed above, gross proceeds for the royalty properties for the third quarter of 2014 exceeded development and production costs thereof, with the portion of such excess attributable to the Trust’s interest in the remaining 15% royalty interest equal to approximately $410,092.  As of July 31, 2014, after applying the net proceeds for the months of May, June and July 2014, the amount by which the aggregate development and production costs for the royalty properties since November 2008 have exceeded the related proceeds of production from the royalty properties has been reduced to approximately $3.6 million (or approximately $2.2 million, net to the Trust’s interest in the remaining 15% royalty interest) as compared to approximately $4.3 million (or approximately $2.6 million, net to the Trust’s interest in the remaining 15% royalty interest) as of April 30, 2014. The Trust will not receive any distribution of net proceeds until such time as the proceeds of production exceed the accumulated excess cost carryforward. As a result, the Trust will not be receiving any net proceeds for the third quarter of 2014.  In light of the continuing expenses of the Trust and the lack of any distributions and any assurances as to the actual timing of any future distributions, the Trustees initiated the Probate Proceeding discussed above and continue to evaluate all alternatives available to the Trust to obtain funds or to reduce the ongoing costs and expenses of the Trust. As a result, there is no guarantee that any further distributions form the Trust will be made.

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 with respect to the royalty properties 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, the Trust’s ability to pay its liabilities, and other factors described in the Trust’s Form 10-K for the year ended December 31, 2013 under “Item 1A. Risk Factors,” as well as other risks identified from time to time in its reports on Form 10-Q and

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Form 8-K as filed with the Securities and Exchange Commission.  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:  Michael J. Ulrich

(512) 236-6599

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