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

Pursuant to Section 906 of the Sarbanes-Oxley Act of 2002 and in connection with the Quarterly Report on Form 10-Q of United Parcel Service, Inc. (the “Corporation”) for the period ended June 30, 2020, as filed with the Securities and Exchange Commission on the date hereof (the “Report”), the undersigned, the Chief Executive Officer of the Corporation, certifies that:

(1)The Report fully complies with the requirements of Section 13(a) or 15(d) of the Securities Exchange Act of 1934; and

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

/S/   CAROL B. TOMÉ

Carol B. Tomé

Chief Executive Officer

(Principal Executive Officer)

August 4, 2020