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 Annual Report on Form 10-K of The Meridian Resource
Corporation (the "Company") for the year ended December 31, 2003, as filed with
the Securities and Exchange Commission on the date hereof (the "Form 10-K"), 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-K 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-K fairly presents, in
                  all material respects, the financial condition and results of
                  operations of the Company.

Date: March 15, 2004

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