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                                                                     EXHIBIT 4.5

                                RIGHTS AGREEMENT
                                 AMENDMENT NO. 2

     THIS AMENDMENT NO.2 TO RIGHTS AGREEMENT is entered into as of February 6,
2002 by Aspen Technology, Inc. (the "Company") and American Stock Transfer and
Trust Company, as Rights Agent (the "Rights Agent"), with respect to the Rights
Agreement dated as of March 12, 1998 between the Company and the Rights
Agreement, as amended to date (the "Rights Agreement").

     WHEREAS, no Distribution Date, as defined in Section 3(b) of the Rights
Agreement, has occurred; and

     WHEREAS, the Company has directed the Rights Agent to enter into this
Amendment No. 2 pursuant to Section 26 of the Rights Agreement;

     NOW, THEREFORE, in consideration of the premises and mutual agreements set
forth herein, the Company and the Rights Agent agree as follows:

     1.  The definition of "Acquiring Person" set forth in Section 1 of the
Rights Agreement is hereby deleted in its entirety and the following is
substituted in lieu thereof:

     "'Acquiring Person' shall mean any Person who or which, alone or together
with all Affiliates and Associates of such Person, shall be the Beneficial Owner
of Common Shares then outstanding that equals or exceeds such Person's Ownership
Threshold, but shall not include (A) the Company, any Subsidiary of the Company,
any employee benefit plan of the Company or of any of its Subsidiaries, or any
Person holding Common Shares for or pursuant to the terms of any such employee
benefit plan, (B) any such Person who or which has become such a Beneficial
Owner solely because (i) of a change in the aggregate number of Common Shares
outstanding since the last date on which such Person acquired Beneficial
Ownership of any Common Shares or (ii) it acquired such Beneficial Ownership in
the good faith belief that such acquisition would not cause such Beneficial
Ownership to exceed such Person's Ownership Threshold and such Person relied in
good faith in computing the percentage of its Beneficial Ownership on publicly
filed reports or documents of the Company which are inaccurate or out-of-date,
or (C) an Exempt Person. Notwithstanding clause (B) of the immediately preceding
sentence, if any Person that is not an Acquiring Person due to such clause (B)
does not reduce its percentage of Beneficial Ownership of Common Shares to an
amount less than such Person's Ownership Threshold by the Close of Business on
the fifth Business Day after notice from the Company (the date of notice being
the first day) that such Person's Beneficial Ownership of Common Shares so
exceeds such Person's Ownership Threshold, such Person shall, at the end of such
five Business Day period, become an Acquiring Person (and such clause (B) shall
no longer apply to such Person). For purposes of this definition, the
determination whether any Person acted in `good faith' shall be conclusively
determined by the Board of Directors of the Company."

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     2. The following definition shall be added to Section 1 of the Rights
Agreement:

     "'Exempt Person' shall mean Pine Ridge Financial Inc., Perseverance LLC and
Smithfield Fiduciary LLC (each a "Series B Investor"), unless and until such
time as such Series B Investor directly or indirectly become the Beneficial
Owner of Common Shares other than Common Shares received (i) as a dividend on,
or as a result of any conversion or redemption of, any shares of the Series B-1
Convertible Preferred Stock, $.10 par value per share, or Series B-2 Convertible
Preferred Stock, $.10 par value per share, of the Company, (ii) upon exercise of
warrants issued by the Company pursuant to the Securities Purchase Agreement,
dated as of the date hereof, between the Company and the Series B Investors, or
(iii) otherwise pursuant to such Securities Purchase Agreement or to the
Registration Rights Agreement, dated as of the date hereof, between the Company
and the Series B Investors. In addition, Exempt Person shall include any Person
to whom or which a Series B Investor transfers any shares of such Series B-1
Convertible Preferred Stock or Series B-2 Convertible Stock or any of such
warrants."

     IN WITNESS WHEREOF, the parties have duly executed this Amendment No. 2 as
of the date first written above.

ASPEN TECHNOLOGY, INC.

By: /s/ Lisa W. Zappala
  -------------------------------------
Name:   Lisa W. Zappala
Title:  Senior Vice President, Finance
        and Chief Financial Officer


AMERICAN STOCK TRANSFER & TRUST COMPANY, as Rights Agent

By: /s/ Herbert L. Lemmer
   ------------------------------------
Name:   Herbert L. Lemmer
Title:  Vice President