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 accompanying Quarterly Report of Greene County
Bancshares, Inc. (the "Company") on Form 10-Q for the quarter ended March 31,
2004 (the "Report"), I, R. Stan Puckett, Chairman of the Board 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; 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/ R. Stan Puckett
                                  --------------------------
                                      R. Stan Puckett
                                      Chairman of the Board and Chief Executive
                                      Officer


Date:  May 7, 2004