Exhibit 3.1

CERTIFICATE OF ELIMINATION
OF THE

SERIES B JUNIOR PARTICIPATING PREFERRED STOCK

OF

BIOCRYST PHARMACEUTICALS, INC.

(Pursuant to Section 151(g) of the
General Corporation Law of the State of Delaware)

BioCryst Pharmaceuticals, Inc., a corporation organized and existing under the General Corporation Law of the State of Delaware (the “Corporation”),

does hereby certify:

That pursuant to Section 151(g) of the General Corporation Law of the State of Delaware (the “DGCL”), the Corporation’s Board of Directors (the “Board”) adopted the following resolutions respecting the Corporation’s Series B Junior Participating Preferred Stock, which resolutions have not been amended or rescinded:

WHEREAS, at a meeting held on June 4, 2002, the Board duly adopted a resolution designating a series of 45,000 shares of Series B Junior Participating Preferred Stock (the “Series B Junior Participating Preferred Stock”);

WHEREAS, at a meeting held on August 5 and 6, 2008, the Board duly adopted a resolution authorizing and directing an increase in the authorized number of shares of Series B Junior Participating Preferred Stock from 45,000 shares to 95,000 shares;

WHEREAS, at a meeting held on February 12, 2014, the Board duly adopted a resolution authorizing and directing an increase in the authorized number of shares of Series B Junior Participating Preferred Stock from 95,000 shares to 200,000 shares;

WHEREAS, a Certificate of the Designation of Series B Junior Participating Preferred Stock was filed in the office of the Secretary of State of the State of Delaware on June 17, 2002, which was amended by a Certificate of Amendment of Certificate of Designation filed in said office on December 20, 2005, a Certificate of Increase of Authorized Number of Shares of Series B Junior Participating Preferred Stock was filed in such office on November 3, 2008, and a Certificate of Increase of Authorized Number of Shares of Series B Junior Participating Preferred Stock was filed in such office on May 5, 2014 (together, the “Certificate of Designation”); and

WHEREAS, the Board deems it advisable and in the best interest of the Corporation and its stockholders to eliminate the Series B Junior Participating Preferred Stock.

NOW, THEREFORE, BE IT RESOLVED, that none of the authorized shares of Series B Junior Participating Preferred Stock are outstanding, and none will be issued subject to the Certificate of Designation;

RESOLVED FURTHER, that the officers of the Corporation be, and each of them hereby is, authorized and directed, in the name and on behalf of the Corporation, to take any and all actions as such officers deem necessary and appropriate to eliminate the Series B Junior Participating Preferred Stock, including to execute and file, or cause to be executed and filed, a Certificate of Elimination of the Series B Junior Participating Preferred Stock with the Secretary of State of the State of Delaware.

That in accordance with Section 151(g) of the DGCL, all matters set forth in the previously filed Certificate of Designation and the Third Restated Certificate of Incorporation of the Corporation with respect to the Series B Junior Participating Preferred Stock are hereby eliminated.

IN WITNESS WHEREOF, BioCryst Pharmaceuticals, Inc. has caused this Certificate to be signed by its duly authorized officer this 12th day of May, 2020.