Exhibit 32.1

Certificate Pursuant to 18 U.S.C. Section 1350, as Adopted
Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002

     I, Carl A. Siebel, the president and chief executive officer of AptarGroup, Inc., certify that (i) the Quarterly Report on Form 10-Q of AptarGroup, Inc. for the quarterly period ended September 30, 2004 (the “Form 10-Q”) fully complies with the requirements of section 13(a) or 15(d) of the Securities Exchange Act of 1934 and (ii) the information contained in the Form 10-Q fairly presents, in all material respects, the financial condition and results of operations of AptarGroup, Inc.

/s/ Carl A. Siebel

Carl A. Siebel
President and Chief Executive Officer

October 29, 2004