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, Peter H. Pfeiffer, the president and chief executive officer of Aptargroup, Inc., certify that (i) the Annual Report on Form 10-K of Aptargroup, Inc. for the year ended December 31, 2010 (the “Form 10-K”) 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-K fairly presents, in all material respects, the financial condition and results of operations of Aptargroup, Inc.

/s/ Peter H. Pfeiffer

Peter H. Pfeiffer

President and Chief Executive Officer

February 25, 2011