Packaging Corporation of America (PKG) S-3ASR Automatic shelf registration

Exhibit 5.1

Mayer Brown LLP 71 South Wacker Drive Chicago, IL 60606 United States of America   T: +1 312 782 0600 F: +1 312 701 7711   mayerbrown.com

September 7, 2021

Packaging Corporation of America

1 North Field Court

Lake Forest, Illinois 60045

Re: Registration Statement on Form S-3

Dear Ladies and Gentlemen:

We have acted as special counsel to Packaging Corporation of America, a Delaware corporation (the “Company”), in connection with the proposed issuance from time to time pursuant to Rule 415 under the Securities Act of 1933, as amended (the “Securities Act”), of the Company’s debt securities (the “Debt Securities”), and the corporate proceedings (the “Corporate Proceedings”) taken and to be taken in connection therewith. Each series of Debt Securities will be issued under an indenture, dated as of July 21, 2003, between the Company and U.S. Bank National Association, as trustee (as supplemented from time to time, the “Indenture”).

We have also participated in the preparation of and filing with the Securities and Exchange Commission (the “Commission”) under the Securities Act of a Registration Statement on Form S-3 (the “Registration Statement”) relating to the Debt Securities. In this connection, we have examined such corporate and other records, instruments, certificates and documents as we considered necessary to enable us to express this opinion. We have assumed the authenticity, accuracy and completeness of all documents, records and certificates submitted to us as originals, the conformity to the originals of all documents, records and certificates submitted to us as copies and the authenticity, accuracy and completeness of the originals of all documents, records and certificates submitted to us as copies. We have also assumed the legal capacity and genuineness of the signatures of persons signing all documents in connection with the opinions set forth below. As to matters of fact (but not as to legal conclusions), to the extent we deemed proper, we have relied on certificates of responsible officers of the Company and of public officials.

Based upon and subject to the foregoing and assuming that (i) the Registration Statement and any amendments thereto (including any post-effective amendments) will have become effective and comply with all applicable laws at the time the Debt Securities are offered or issued as contemplated by the Registration Statement, (ii) a prospectus supplement, pricing supplement

Mayer Brown is a global services provider comprising an association of legal practices that are separate entities including

Mayer Brown LLP (Illinois, USA), Mayer Brown International LLP (England), Mayer Brown (a Hong Kong partnership)

and Tauil & Chequer Advogados (a Brazilian partnership).

Mayer Brown LLP

Packaging Corporation of America

September 7, 2021

Page 2

and/or term sheet will have been prepared and filed with the Commission describing the series of Debt Securities offered thereby and will at all relevant times comply with all applicable laws, (iii) all Debt Securities will be issued and sold in compliance with applicable federal and state securities laws and in the manner stated in the Registration Statement and the appropriate prospectus supplement, pricing supplement and/or term sheet, (iv) a definitive purchase, underwriting or similar agreement and any other necessary agreement with respect to any Debt Securities will have been duly authorized and validly executed and delivered by the Company and the other party or parties thereto, (v) the board of directors, including any appropriate committee appointed thereby, and appropriate officers of the Company have taken all necessary action to approve the issuance and terms of the Debt Securities and related matters, (vi) the Indenture has been duly qualified under the Trust Indenture Act of 1939, as amended, and (vii) the terms of any Debt Securities will not violate any applicable law or result in a default under or breach of any agreement or instrument binding upon the Company and such terms comply with any requirement or restriction imposed by any court or governmental body having jurisdiction over the Company, we advise you that in our opinion that upon the completion of the Corporate Proceedings relating to a series of Debt Securities, the due execution, authentication, issuance and delivery of the Debt Securities of such series, and the receipt of the consideration therefor, the Debt Securities of such series will constitute valid and legally binding obligations of the Company entitled to the benefits of the applicable Indenture and will be enforceable against the Company in accordance with the terms of such series of Debt Securities, except that (a) the enforceability thereof may be subject to (i) bankruptcy, insolvency, reorganization, moratorium, fraudulent conveyance or other similar laws now or hereafter in effect relating to or affecting creditors’ rights or remedies generally and (ii) general principles of equity and to the discretion of the court before which any proceedings therefor may be brought (regardless of whether enforcement is sought in a proceeding at law or in equity) and (b) the enforceability of provisions imposing liquidated damages, penalties or an increase in interest rate upon the occurrence of certain events may be limited in certain circumstances.

We hereby consent to the filing of this opinion as an exhibit to the Registration Statement and to being named in the related prospectus under the caption “Legal Matters” with respect to the matters stated therein. In giving this consent, we do not thereby 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 under Section 7 of the Securities Act or the rules and regulations of the Commission.

We express no opinion as to matters under or involving any laws other than the laws of the State of Illinois, the laws of the State of New York, the General Corporation Law of the State of Delaware and the federal laws of the United States of America.

This opinion is limited to the specific issues addressed herein, and no opinion may be inferred or implied beyond that expressly stated herein. This opinion expressed herein is as of the date hereof. We assume no obligation to revise or supplement this opinion should the present laws of the United States be changed by legislative action, judicial decision or otherwise or to reflect any facts or circumstances that may hereafter come to our attention.

Mayer Brown LLP

Packaging Corporation of America

September 7, 2021

Page 3

This opinion is furnished in connection with the filing of the Registration Statement and is not to be used, circulated, quoted or otherwise relied upon for any other purpose.

Very truly yours,

/s/ Mayer Brown LLP

Mayer Brown LLP