Exhibit 3.1

SECOND AMENDMENT TO RIGHTS AGREEMENT

Amendment dated as of October [22], 2014 (this “Second Amendment”) to the Rights Agreement, dated as of March 22, 1999, as amended by the First Amendment dated as of March 12, 2009 (the “Rights Agreement”), between American Shared Hospital Services, a California corporation (the “Company”), and American Stock Transfer & Trust Company, as Rights Agent (the “Rights Agent”). Capitalized terms used herein and not defined shall have the meanings specified in the Rights Agreement.

WHEREAS, the Company and the Rights Agent are parties to the Rights Agreement;

WHEREAS, Section 27 of the Rights Agreement permits the Company to amend the Rights Agreement on the terms set forth in this Second Amendment;

WHEREAS, the Board of Directors of the Company has determined that it is in the best interests of the Company and its shareholders to modify the terms of the Rights Agreement as set forth in this Second Amendment and in connection therewith the Company is entering into this Second Amendment and directing the Rights Agent to enter into this Second Amendment; and

WHEREAS, all acts and things necessary to make this Second Amendment a valid agreement, enforceable according to its terms have been done and performed, and the execution and delivery of this Second Amendment by the Company and the Rights Agent have been in all respects duly authorized by the Company and the Rights Agent.

NOW, THEREFORE, in consideration of the promises and mutual agreements set forth herein, and for other good and valuable consideration, the receipt and sufficiency of which are hereby acknowledged, and intending to be legally bound, the Company and the Rights Agent hereby agree as follows:

A. Amendment of Section 1. The last sentence of Section 1(a) of the Rights Agreement is hereby deleted in its entirety and replaced with the following sentence:

“Notwithstanding the foregoing, (i) if the Board of Directors of the Company determines in good faith that a Person who would otherwise be an "Acquiring Person" (as defined pursuant to the foregoing provisions of this paragraph (a)) has become such inadvertently, and such Person divests as promptly as practicable a sufficient number of shares of Common Stock so that such Person would no longer be an "Acquiring Person" (as defined pursuant to the foregoing provisions of this paragraph (a)), then such Person shall not be deemed to be an "Acquiring Person" for any purposes of this Agreement; and (ii) neither Raymond C. Stachowiak nor John F. Ruffle (together, the “Fourth Milestone Investors”) shall be deemed to become an “Acquiring Person” (as defined pursuant to the foregoing provisions of this paragraph (a)) as the result of an acquisition of shares of Common Stock in connection with the Fourth Milestone Investment, including shares of Common Stock acquired upon exercise of the warrants received as part of the Fourth Milestone Investment.”

In addition, the following paragraph shall be added after paragraph (g) as paragraph (h) and the subsequent paragraphs shall be relettered accordingly:

“(h) Fourth Milestone Investment” shall mean (i) the Company’s issuance of promissory notes and warrants to the Fourth Milestone Investors pursuant to a Note and Warrant Purchase Agreement dated as of October 22, 2014 by and between the Company and the Fourth Milestone Investors and (ii) the Company’s sale of shares of Common Stock to Mr. Stachowiak pursuant to a Common Stock Purchase Agreement dated as of October 22, 2014 by and between the Company and Mr. Stachowiak.

B. Effect of Amendment. Except as expressly set forth herein, the Rights Agreement shall not by implication or otherwise be supplemented or amended by virtue of this Second Amendment, but shall remain in full force and effect, as amended hereby. This Second Amendment shall be construed in accordance with and as a part of the Rights Agreement, and all terms, conditions, representations, warranties, covenants and agreements set forth in the Rights Agreement and each other instrument or agreement referred to therein, except as herein amended, are hereby ratified and confirmed. To the extent that there is a conflict between the terms and provisions of the Rights Agreement and this Second Amendment, the terms and provisions of this Second Amendment shall govern for purposes of the subject matter of this Second Amendment only.

C. Waiver of Notice. The Rights Agent and the Company hereby waive any notice requirement with respect to each other under the Rights Agreement, if any, pertaining to the matters covered by this Second Amendment.

D. Severability. If any provision, covenant or restriction of this Second Amendment is held by a court of competent jurisdiction or other authority to be invalid, illegal or unenforceable, the remainder of the terms, provisions, covenants and restrictions of this Second Amendment shall remain in full force and effect and shall in no way be effected, impaired or invalidated.

E. Governing Law. This Second Amendment shall be deemed to be a contract made under the laws of the State of California and for all purposes shall be governed by and construed in accordance with the laws of such state applicable to contracts to be made and performed entirely within such state, except that the rights and obligations of the Rights Agent shall be governed by the law of the State of New York.

F. Counterparts. This Second Amendment may be executed in any number of counterparts and each of such counterparts shall for all purposes be deemed to be an original, and all such counterparts shall together constitute but one and the same instrument.

G. Effective Date of Amendment. This Second Amendment shall be deemed effective as of the date first written above, as if executed on such date.

H. Descriptive Headings. Descriptive headings appear herein for convenience only and shall not control or affect the meaning or construction of any of the provisions hereof.

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IN WITNESS WHEREOF, the parties hereto have caused this Second Amendment to be duly executed as of the date first written above.