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 / (512) 236-6599 / AUSTIN, TEXAS 78701

TEL OFFSHORE TRUST PROVIDES UPDATES ON FUTURE QUARTERLY DISTRIBUTIONS AND PROBATE PROCEEDING

AUSTIN, TEXAS July 18, 2016—TEL OFFSHORE TRUST (the “Trust”) announced that as a result of the recent sale by the TEL Offshore Trust Partnership (the “Partnership”) of the Partnership’s remaining overriding royalty interests (the “Royalty Sale”) there will be no trust distribution for the second quarter of 2016 for unitholders of record on June 30, 2016 and the Trust will not be making further distributions unless and until approved in the previously disclosed probate proceeding as described below.  Since the Royalty Sale was effective February 1, 2016, the purchaser of the overriding royalty interests (the “Royalty Interests”) is entitled to receive all proceeds from the Royalty Interests from and after February 1, 2016.  Accordingly, the Trust will not issue any further quarterly press releases regarding the financial and operating information of the oil and gas properties burdened by the Royalty Interest.

As previously disclosed, on July 10, 2014, the trustees of the Trust (the “Trustees”) filed a Petition for Modification and Termination of the Trust (the “Petition”) with the Probate Court of Travis County, Texas (the “Court”). The Petition requested that the Court modify the Trust’s 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 unit holder approval to (a) sell all or any portion of the Trust’s interests in 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 Partnership’s remaining overriding royalty interest.  The Royalty Sale was made in accordance with that certain Final Judgment and Order entered by the Court on January 15, 2016 (the “Order”) pursuant to which the Court ordered that the Trustees of the Trust to direct the Partnership to sell all of the Royalty Interests owned by the Partnership on or before June 30, 2016.  All remaining matters, including the attorney ad litem’s request for an accounting and the issues concerning termination of the Trust (the “Remaining Matters”), were continued to a later date.  Due to the Remaining Matters, the Trust must hold the net proceeds in a segregated account until the Court’s final resolution of the Remaining Matters.

The attorney ad litem is pursuing discovery regarding the Remaining Matters and he has threatened to assert additional claims against the Trustees. The Trustees are in the process of responding to the attorney ad litem’s requests.  The parties have scheduled a mediation of the Remaining Matters on August 18, 2016 and the Remaining Matters are set for trial on November 7, 2016.  The disposition of the net proceeds from the Royalty Sale will be made in accordance with the final resolution of the Remaining Matters.

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.

This press release contains forward-looking statements, including statements relating to the Remaining Matters and any disposition of the net proceeds from the Royalty Sale.  Important factors that could cause these statements to differ materially include the outcome of the pending Remaining Matters before the Court, 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, 2015 under “Item 1A. Risk Factors,” as well as other risks identified from time to time in its reports on Form 10-Q and Form 8-K as filed with the SEC.  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

2