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

The undersigned, Jean-Pierre M. Ergas, Chairman and Chief Executive Officer of BWAY Corporation (the “Company”) and Kevin C. Kern, Vice-President of Administration and Chief Financial Officer of the Company, certify, pursuant to Section 906 of the Sarbanes-Oxley Act of 2002, 18 U.S.C. Section 1350, that:

(1) The quarterly report on Form 10-Q of the Company for the quarter ended April 4, 2004 (the “Report”) fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934 (15 U.S.C. 78m or 78o(d)); and

(2) The information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

Dated: May 14, 2004

/s/ Jean-Pierre M. Ergas

Jean-Pierre M. Ergas

Chairman and Chief Executive Officer

/s/ Kevin C. Kern

Kevin C. Kern

Vice-President of Administration and

Chief Financial Officer