EXHIBIT 32.1

                    CERTIFICATION OF CHIEF EXECUTIVE OFFICER
     PURSUANT TO RULE 13a-14(b) OR RULE 15d-14(b) AND 18 U.S.C. SECTION 1350

In connection with the Quarterly Report on Form 10-Q of The Meridian Resource
Corporation (the "Company") for the quarter ended March 31, 2004, as filed with
the Securities and Exchange Commission on the date hereof (the "Form 10-Q"), I,
Joseph A. Reeves, Jr., Chief Executive Officer of the Company, certify pursuant
to Section 906 of the Sarbanes-Oxley Act of 2002, that:

1.       The Form 10-Q fully complies with the requirements of Section 13(a) or
         15(d) of the Securities Exchange Act of 1934; and

2.       The information contained in the Form 10-Q fairly presents, in all
         material respects, the financial condition and results of operations of
         the Company.

         Date: May 5, 2004

                                             /s/ Joseph A. Reeves, Jr.
                                             -----------------------------------
                                             Joseph A. Reeves, Jr.
                                             Chief Executive Officer

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