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Exhibit 32.2

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 Annual Report of Stone Container Corporation (the "Company") on Form 10-K for the period ending December 31, 2003 as filed with the Securities and Exchange Commission on the date hereof (the "Report"), I, Charles A. Hinrichs, Vice President and Chief Financial Officer of the Company, certify, pursuant to 18 U.S.C. § 1350, as adopted pursuant to § 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 result of operations of the Company.

/s/  CHARLES A. HINRICHS Charles A. Hinrichs
Vice President and Chief Financial Officer
March 3, 2004

        A signed original of this written statement required by Section 906, or other document authenticating, acknowledging or otherwise adopting the signature that appears in typed form within the electronic version of this written statement required by Section 906, has been provided to Stone Container Corporation and will be retained by Stone Container Corporation and furnished to the Securities and Exchange Commission or its staff upon request.

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Exhibit 32.2