Exhibit 99.1

Sabine Royalty Trust

News Release                        

SABINE ROYALTY TRUST ANNOUNCES

MONTHLY CASH DISTRIBUTION FOR MAY

Dallas, Texas, May 4, 2016 – Southwest Bank, as Trustee of the Sabine Royalty Trust (NYSE: SBR), today declared a cash distribution to the holders of its units of beneficial interest of $0.16435 per unit, payable on May 27, 2016, to unit holders of record on May 16, 2016. Sabine’s cash distribution history, current and prior year financial reports and tax information booklets, a link to filings made with the Securities and Exchange Commission and more can be found on its website at http://www.sbr-sabine.com/.

This distribution reflects primarily the oil production for February 2016 and the gas production for January 2016. Preliminary production volumes are approximately 42,357 barrels of oil and 602,962 Mcf of gas. Preliminary prices are approximately $32.62 per barrel of oil and $2.65 per Mcf of gas.

The table below compares this month’s production and prices to the previous month’s:

Revenues are only posted and distributed when they are received. Most energy companies normally issue payment of royalties on or about the 25^th of every month, and depending on mail delivery, a varying amount of royalties are not received until after the revenue posting on the last business day of the month. The revenues received after that date will be posted within 30 days of receipt.

Due to the timing of the end of the month of April, approximately $439,000 of revenue received will be posted in the following month of May in addition to normal receipts during May. Since the close of business in April and prior to this press release, approximately $64,000 in revenue has been received.

*      *      *