Exhibit 5.1

77 WEST WACKER “ SUITE 3500 “ CHICAGO, ILLINOIS 60601.1692

TELEPHONE: +1.312.782.3939 • FACSIMILE: +1.312.782.8585

February 24, 2021

ANSYS, Inc.

2600 ANSYS Drive

Canonsburg, PA 15317

Re: Registration Statement on Form S-3 Filed by ANSYS, Inc.

Ladies and Gentlemen:

We have acted as counsel for ANSYS, Inc., a Delaware corporation (the “Company”), in connection with the registration for resale from time to time by certain of the Company’s stockholders (the “Selling Stockholders”) of (1) 641,400 shares (the “Initial Shares”) of common stock, $0.01 par value per share, of the Company (“Common Stock”) issued

pursuant to the Agreement and Plan of Merger, dated as of October 23, 2020 (the “Merger Agreement”), by and among ANSYS, Inc., Voyager Merger Sub, Inc., Analytical Graphics, Inc. and Fortis Advisors LLC, as Shareholder’s Representative, and (2) 24,297 shares (the “Escrowed Shares” and, together with the Initial Shares, the “Shares”) that may be delivered to the Selling Stockholders pursuant to the Merger Agreement, in each case as contemplated by the Company’s Registration Statement on Form S-3 to which this opinion is filed as an exhibit (as the same may be amended from time to time, the “Registration Statement”). The Shares may be offered and sold from time to time pursuant to Rule 415 under the Securities Act of 1933 (the “Securities Act”).

In connection with the opinion expressed herein, we have examined such documents, records and matters of law as we have deemed relevant or necessary for purposes of this opinion. Based on the foregoing, and subject to the further limitations, qualifications and assumptions set forth herein, we are of the opinion that:

1. The Initial Shares have been validly issued and are fully paid and nonassessable.

2. The Escrowed Shares, when issued and delivered in accordance with the terms of the Merger Agreement, will be validly issued, fully paid and nonassessable.

The opinions set forth above are subject to the following limitations, qualifications and assumptions.

In rendering the foregoing opinions, we have assumed that the resolutions authorizing the Company to issue and deliver the Escrowed Shares pursuant to the Merger Agreement by the Company’s Board of Directors (or an authorized committee thereof) will be in full force and effect at all times at which such Shares are issued and delivered by the Company, and the Company will take no action inconsistent with such resolutions.

AMSTERDAM • ATLANTA • BEIJING • BOSTON • BRISBANE • BRUSSELS • CHICAGO • CLEVELAND • COLUMBUS • DALLAS • DETROIT

DUBAI • DUSSELDROF • FRANKFURT • HONGKONG • HOUSTON • IRVINE • LONDON • LOS ANGELES • MADRID • MELBOURNE

MEXICO CITY • MIAMI • MILAN • MINNEAPOLIS • MOSCOW • MUNICH • NEWYORK • PARIS • PERTH • PITTSBURGH • SAN DIEGO

SAN FRANSICO • SAO PAULO • SAUDI ARABIA • SHANGHAI • SILICON VALLEY • SINGAPORE • SYDNEY • TAIPEI • TOKYO • WASHIINGTTON

As to facts material to the opinions and assumptions expressed herein, we have relied upon oral or written statements and representations of officers and other representatives of the Company and others. We have further assumed the regularity of all corporate actions and proceedings.

The opinion expressed herein is limited to the laws of the State of Delaware, as currently in effect, and we express no opinion as to the effect of the laws of any other jurisdiction on the opinion expressed herein.

We hereby consent to the filing of this opinion as Exhibit 5.1 to the Registration Statement and to the reference to Jones Day under the caption “Legal Matters” in the prospectus constituting a part of the Registration Statement. In giving such consent, we do not thereby admit that we are included in the category of persons whose consent is required under Section 7 of the Securities Act or the rules and regulations of the Securities and Exchange Commission promulgated thereunder.

Very truly yours,

/s/ Jones Day