EXHIBIT 32.1

                                CERTIFICATION OF
                      PRESIDENT AND CHIEF EXECUTIVE OFFICER
                         OF RANGE RESOURCES CORPORATION
                       PURSUANT TO 18 U.S.C. SECTION 1350

In connection with the accompanying report on Form 10-Q for the period ending
March 31, 2004 and filed with the Securities and Exchange Commission on the date
hereof (the "Report"), I, John H. Pinkerton, President and Chief Executive
Officer of Range Resources Corporation (the "Company"), hereby certify that:

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

                                               By: /s/ JOHN H. PINKERTON
                                                   ---------------------------
                                                   John H. Pinkerton
                                                   May 4, 2004