Exhibit 5.1

September 15, 2016

Bemis Company, Inc.

One Neenah Center, 4th Floor

P.O. Box 669

Neenah, Wisconsin 54957-0669

Ladies and Gentlemen:

We have acted as counsel for Bemis Company, Inc., a Missouri corporation (the “Company”), in connection with a Registration Statement on Form S-3 (Registration No. 333-213475) (the “Registration Statement”), including the prospectus constituting a part thereof, dated September 2, 2016, and the prospectus supplement, dated September 8, 2016 (collectively, the “Prospectus”), filed by the Company with the Securities and Exchange Commission under the Securities Act of 1933, as amended (the “Securities Act”), relating to the issuance and sale by the Company of $300,000,000 aggregate principal amount of the Company’s 3.100% Senior Notes due 2026 (the “Securities”) in the manner set forth in the Registration Statement and the Prospectus.  The Securities have been issued under an Indenture, dated as of June 15, 1995 (the “Indenture”), between the Company and U.S. Bank National Association (formerly known as First Trust National Association), as trustee (the “Trustee”) and the related Certificate of Designated Officers Establishing Terms of a Series of Securities Under Open-End Indenture, dated September 15, 2016 (the “Certificate of Designated Officers”).

As counsel to the Company in connection with the issuance and sale of the Securities, we have examined: (i) the Registration Statement, including the Prospectus and the exhibits (including those incorporated by reference) constituting a part of the Registration Statement; (ii) the Indenture and the Certificate of Designated Officers; (iii) the Securities; and (iv) such other proceedings, documents and records as we have deemed necessary to enable us to render the opinions set forth below.

In our examination of the above-referenced documents, we have assumed the genuineness of all signatures, the authenticity of all documents, certificates and instruments submitted to us as originals and the conformity with the originals of all documents submitted to us as copies.

Based upon and subject to the foregoing and the other matters set forth herein, assuming that (i) the Indenture has been duly authorized, executed and delivered by, and represents the valid and binding obligation of, the Trustee and (ii) the Securities have been duly authenticated by the Trustee, and having regard for such legal considerations as we deem relevant, we are of the opinion that the Securities, when delivered by the Company in the manner and for the consideration contemplated by the Registration Statement and the Prospectus, will be legally issued and valid and binding obligations of the Company, enforceable against the Company in accordance with their

terms, subject to bankruptcy, insolvency, fraudulent transfer, reorganization, moratorium and similar laws of general applicability relating to or affecting creditors’ rights and to general equity principles (regardless of whether enforcement is considered in a proceeding in equity or at law).

We express no opinion as to any provision of any instrument, agreement or other document (i) regarding severability of the provisions thereof or (ii) providing that the assertion or employment of any right or remedy shall not prevent the concurrent assertion or employment of any other right or remedy, or that every right and remedy shall be cumulative and in addition to every other right and remedy, or that any delay or omission to exercise any right or remedy shall not impair any right or remedy or constitute a waiver thereof.

We are qualified to practice law in the States of Wisconsin, New York and Missouri.  We express no opinion with respect to the laws of any jurisdiction other than the States of Wisconsin and New York, the provisions of The General and Business Corporation Law of the State of Missouri and the federal laws of the United States of America.

We hereby consent to the deemed incorporation by reference of this opinion into the Registration Statement and the Prospectus and to the references to our firm therein.  In giving this consent, we do not admit that we are “experts” within the meaning of Section 11 of the Securities Act or within the category of persons whose consent is required by Section 7 of the Securities Act.

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