UNITED STATES SECURITIES AND EXCHANGE

COMMISSION

Washington, D.C. 20549

FORM 6-K

REPORT OF FOREIGN PRIVATE ISSUER

PURSUANT TO RULE 13a-16 OR 15d-16 UNDER

THE SECURITIES EXCHANGE ACT OF 1934

For the month of June, 2022

Commission File Number: 001-40709

Ardagh Metal Packaging S.A.

(Name of Registrant)

56, rue Charles Martel
L-2134 Luxembourg, Luxembourg
+352 26 25 85 55

(Address of Principal Executive Offices)

Indicate by check mark whether the registrant files or will file annual reports under cover of Form 20-F or Form 40-F.

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(1): ¨

Indicate by check mark if the registrant is submitting the Form 6-K in paper as permitted by Regulation S-T Rule 101(b)(7): ¨

EXHIBIT INDEX

The following exhibit is filed as part of this Form 6-K:

SIGNATURES

Pursuant to the requirements of the Securities Exchange Act of 1934, Ardagh Metal Packaging S.A. has duly caused this report to be signed on its behalf by the undersigned, thereunto duly authorized.

Date: June 17, 2022