EXHIBIT 32.1
                                                                    ------------

                           CERTIFICATION PURSUANT TO
                             18 U.S.C. SECTION 1350
                             AS ADOPTED PURSUANT TO
                 SECTION 906 OF THE SARBANES-OXLEY ACT OF 2002


     In connection with the periodic report of Dawson Geophysical Company (the
"Company") Form 10-K for the period ending September 30, 2003 as filed with the
Securities and Exchange Commission on the date hereof (the "Report"), I, L.
Decker Dawson, Chairman and Chief Executive Officer of the Company, certify,
pursuant to 18 U.S.C. Section 1350, as adopted pursuant to Section 906 of the
Sarbanes-Oxley Act of 2002, that:

     (1)  The Report fully complies with the requirements of Section 13 (a) or
          15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or
          78o(d)); and

     (2)  The information contained in the Report fairly presents, in all
          material respects, the financial condition and results of operations
          of the Company.



Dated: November 28, 2003               /s/ L. Decker Dawson
                                       -----------------------------------------
                                       Chairman and Chief Executive Officer