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 on Form 10-Q of Rock-Tenn Company (the “Corporation”), for the quarter ended March 31, 2010, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned, James A. Rubright, Chairman of the Board and Chief Executive Officer of the Corporation, and Steven C. Voorhees, Executive Vice President, Chief Financial Officer and Chief Administrative Officer of the Corporation, each 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 Corporation.