Exhibit 32.1

CERTIFICATION OF CHIEF EXECUTIVE OFFICER

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 (18 U.S.C. § 1350), the undersigned, James P. McNiel, Chief Executive Officer of FalconStor Software, Inc., a Delaware Corporation (the “Company”), does hereby certify, to his knowledge, that:

The Annual Report on Form 10-K for the year ended December 31, 2012 of the Company (the “Report”) fully complies with the requirements of Sections 13(a) and 15(d) of the Securities Exchange Act of 1934, and the information contained in the Report fairly presents, in all material respects, the financial condition and results of operations of the Company.

/s/ James P. McNiel

President and Chief Executive Officer

March 18, 2013