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 quarterly report of Dawson Geophysical Company (the “Company”) on Form 10-Q for the period ended December 31, 2014, as filed with the Securities and Exchange Commission (the “Report”), I, Stephen C. Jumper, President, 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 to my knowledge:

(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: February 6, 2015

/s/ Stephen C. Jumper

Stephen C. Jumper

Chairman of the Board of Directors, President and

Chief Executive Officer

(principal executive officer)