Bemis 10-Q 2008 Q2 Quarterly report

EXHIBIT 32

SECTION 1350 CERTIFICATIONS OF CEO AND CFO

                Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, each of the undersigned certifies that the quarterly report on Form 10-Q of Bemis Company, Inc. for the quarter ended June 30, 2008 (the “Report”), fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 and that information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of Bemis Company, Inc.

/s/ Henry J. Theisen	/s/ Gene C. Wulf
Henry J. Theisen, President and	Gene C. Wulf, Senior Vice President and
Chief Executive Officer	Chief Financial Officer
August 5, 2008	August 5, 2008