THE MERIDIAN RESOURCE CORPORATION
                   SHAREHOLDERS APPROVE SHELL TRANSACTIONS

      The Meridian Resource Corporation (NYSE:TMR) announced today that,
following approval of its shareholders, it consummated the previously announced
merger (the "Merger") of Louisiana Onshore Properties Inc., an indirect
subsidiary of Shell Oil Company ("Shell"), and LOPI Acquisition Corp., a
wholly-owned subsidiary of Meridian. Meridian also announced that, immediately
following consummation of the Merger, it completed a separate purchase (with the
Merger, the "Shell Transactions") of oil and gas property interests from a
subsidiary of Shell. Consummation of the Shell Transactions provides Meridian
with substantially all of Shell's and its direct and indirect subsidiaries'
onshore oil and gas property interests in south Louisiana, and access to
substantially all of Shell's and its direct and indirect subsidiaries' 2-D and
3-D seismic data covering onshore south Louisiana. In connection with the
Merger, affiliates of Shell received a 39.9% interest in the Company, assuming
exercise of all outstanding options and warrants, comprised of 12,082,030 shares
of common stock and shares of a new series of preferred stock convertible into
12,837,428 shares of common stock. Meridian paid $42.5 million in connection
with the separate acquisition of oil and gas property interests, subject to
adjustment for production, expenses and other items since October 1, 1997.

      Joe Reeves, Chairman and CEO of Meridian, stated "We are very excited
about this new relationship with Shell. The addition of the oil and gas property
interests acquired in the Shell Transactions significantly strengthens the
Company's presence and operating leverage in the south Louisiana oil and gas
producing region."

      Transition of the operations of the properties acquired in the Shell
Transactions and analysis of the extensive 3-D and 2-D seismic data began with
the execution of a Transition Management Agreement on May 21, 1998.
Exploration/exploitation activities on the Shell properties have resulted in
field production increases of approximately 13 MMCFe/D plus two discoveries, as
follows:

      o     On May 15, 1998, Meridian, as Operator and 25% working interest
            owner of the West Gueydan prospect, completed the Anna Belle Bourque
            #1, in the Marg Howei sand at a depth of 12,500 feet. The well was
            tested at 3,377 MCF/D, 218 BC/D and 62 BW/D through a 14/64" choke
            at 3,520 psi FTP. Two additional wells are planned for the West
            Gueydan prospect in 1998, including the Vermillion Parish School
            Board No. 1 well, which currently is drilling at 10,002 feet with a
            planned total depth of 15,700 feet.

      o     On June 29, 1998, Meridian, as Operator and 100% working interest
            owner, logged the Myles Salt No. 32 at a total depth of 7,440 feet.
            Electric log analysis indicates the presence of 551 feet of gross
            pay. Two development wells are currently planned following
            completion of the No. 32 well.

      Meridian also announced that the voting on the proposal to increase
Meridian's authorized shares of common stock from 100,000,000 to 200,000,000
shares was deferred to give shareholders additional time to vote on the
proposal. The Special Meeting of Shareholders will reconvene on July 20, 1998,
at 9:00 a.m., at Meridian's offices to complete voting on such proposal.

      The Meridian Resource Corporation is an independent oil and natural gas
company engaged in the exploration and development of oil and natural gas
properties utilizing 3-D seismic technology, primarily in south Louisiana,
southeast Texas and offshore Gulf of Mexico. Meridian's offices are located in
Houston, Texas and its common stock is traded on the New York Stock Exchange
under the symbol "TMR". For additional information, visit our website at
WWW.TMRC.COM or our E-mail address at TMRC@IX.NETCOM.COM.

      Certain of the foregoing statements may be deemed "forward-looking
statements" within the meaning of the Securities Exchange Act of 1934. Although
Meridian believes that the expectations reflected in such forward-looking
statements are reasonable, there can be no assurance that such expectations will
prove to have been correct. Certain risks and uncertainties inherent in
Meridian's business are set forth in Meridian's filings with the Securities and
Exchange Commission. These risks include (i) the continued production from
existing wells at their current or projected levels, (ii) price changes for oil
and gas, (iii) the ability of the Company to successfully complete those wells
that have been logged and reflect potential production, (iv) the ability of the
Company to successfully complete and produce those reserves scheduled as
"non-producing" or "undeveloped", (v) the ability of the Company to acquire
leases and timely drill its exploratory prospects, (vi) risks regarding
estimates of reserves, (vii) production risks, (viii) governmental regulations
and (ix) general risks regarding the exploration for, and production of, oil and
gas reserves, including uncertainties with respect to preliminary logging and
well tests.

      CONTACT: Meridian Resource Corporation, Houston Joseph A. Reeves, Jr.,
               Michael J. Mayell or P. Richard "Dick" Gessinger, 281/558-8080