Georesources (GEOI) 10-Q 2011 Q2 Quarterly report

Exhibit 32.1

Certification

I, Frank A. Lodzinski, certify that:

In connection with the Quarterly Report on Form 10-Q of GeoResources, Inc. (the “Company”) for the period ended June 30, 2011, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), I, Frank A. Lodzinski, 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, as amended; and

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

/s/ Frank A. Lodzinski

Frank A. Lodzinski

Chief Executive Officer

August 8, 2011

* The foregoing certification is being furnished solely pursuant to 18 U.S.C. Section 1350 and is not being filed as part of the Report or as a separate disclosure document.