EXHIBIT 10.9

TWENTIETH LOAN MODIFICATION AGREEMENT

This Twentieth Loan Modification Agreement (this “Loan Modification Agreement”) is entered into on May 15, 2008 by and between SILICON VALLEY BANK, a California chartered bank, with its principal place of business at 3003 Tasman Drive, Santa Clara, California 95054 and with a loan production office located at One Newton Executive Park, Suite 200, 2221 Washington Street, Newton, Massachusetts  02462 (“Bank”) and ASPEN TECHNOLOGY, INC., a Delaware corporation with offices at 200 Wheeler Road, Burlington, Massachusetts 01803 for itself and as successor by merger with ASPENTECH, INC., a Texas corporation with offices at 200 Wheeler Road, Burlington, Massachusetts 01803 (“Borrower”).

1.                                       DESCRIPTION OF EXISTING INDEBTEDNESS AND OBLIGATIONS.  Among other indebtedness and obligations which may be owing by Borrower to Bank, Borrower is indebted to Bank pursuant to a loan arrangement dated as of January 30, 2003, evidenced by, among other documents, a certain Loan and Security Agreement dated as of January 30, 2003 between Borrower, Aspentech, Inc. and Bank, as amended by a certain letter agreement dated February 14, 2003, a certain First Loan Modification Agreement dated June 27, 2003, a certain Second Loan Modification Agreement dated September 10, 2004, a certain Third Loan Modification Agreement dated January 28, 2005, a certain Fourth Loan Modification Agreement dated April 1, 2005, a certain Fifth Loan Modification Agreement dated May 6, 2005, a certain Sixth Loan Modification Agreement dated June 15, 2005, a certain Seventh Loan Modification Agreement dated September, 2005, a certain Eighth Amendment to Loan and Security Agreement dated November 22, 2005, a certain Ninth Loan Modification Agreement dated July 17, 2006, a certain Tenth Loan Modification Agreement dated September 15, 2006, a certain Eleventh Loan Modification Agreement dated September 27, 2006, a certain Twelfth Loan Modification Agreement dated January 12, 2007, a certain Thirteenth Loan Modification Agreement dated April 13, 2007, a certain Fourteenth Loan Modification Agreement dated June 28, 2007, a certain Waiver Agreement dated June 28, 2007, a certain Fifteenth Loan Modification Agreement dated August 30, 2007, a certain Sixteenth Loan Modification Agreement dated October 16, 2007, a certain Seventeenth Loan Modification Agreement dated December 28, 2007,  a certain Eighteenth Loan Modification Agreement dated January 24, 2008 and a certain Nineteenth Loan Modification Agreement dated April 11, 2008 (as amended, the “Loan Agreement”).  Capitalized terms used but not otherwise defined herein shall have the same meaning as in the Loan Agreement.

2.                                       DESCRIPTION OF COLLATERAL.  Repayment of the Obligations is secured by the Collateral as described in the Loan Agreement (together with any other collateral security granted to Bank, the “Security Documents”).

Hereinafter, the Security Documents, together with all other documents evidencing or securing the Obligations shall be referred to as the “Existing Loan Documents”.

3.                                       DESCRIPTION OF CHANGE IN TERMS.

Modifications to Loan Agreement.

(i)                                     The Loan Agreement shall be amended by inserting the following new definitions to appear alphabetically in Section 8 thereof:

““APP Facilities” means any collateralized obligations under any accounts receivable purchase agreement existing as of the date hereof between Borrower any other party, including, without limitation, that certain Non Recourse Receivables Purchase Agreement by and between Borrower and Silicon, dated as of December 31, 2003, as amended and as may be further amended and in effect from time to time.”

(ii)                                  The Loan Agreement shall be amended by deleting the following text appearing in Section 4 of the Schedule to the Loan Agreement:

“MATURITY DATE

(Section 6.1):         May 15, 2008”

and inserting in lieu thereof the following:

“MATURITY DATE

(Section 6.1):         November 15, 2008”

(iii)                               The Loan Agreement shall be amended by deleting the following text appearing in Section 5 of the Schedule thereto:

““Adjusted Quick Ratio” is the ratio of (i) Quick Assets to (ii) Current Liabilities plus the face amount of all issued Letters of Credit, less the current portion of Deferred Revenue and other income received in advance, less the outstanding principal balance of all debt subordinated to the Obligations on terms satisfactory to Silicon.

“Quick Assets” is, on any date, the Borrower’s consolidated, unrestricted cash, cash equivalents, net billed accounts receivable (plus the current portion of long-term installment receivables, net of unamortized discounts)  and investments with maturities of fewer than 12 months determined according to GAAP.”

and inserting in lieu thereof the following:

“Adjusted Quick Ratio” is the ratio of (i) Quick Assets to (ii) Current Liabilities (including, without limitation or duplication, that portion of the outstanding Obligations under this Agreement that would otherwise constitute Current Liabilities) plus, without duplication, the face amount of all issued Letters of Credit, less the current portion of Deferred Revenue and other income from installment receivables received in advance, less the outstanding principal balance of debt secured by collateralized receivables pursuant to the APP Facilities.”

“Quick Assets” is, on any date, the Borrower’s (i) consolidated, unrestricted cash and cash equivalents, plus (ii) net billed accounts receivable (including the current portion of long-term installment receivables (net of unamortized discounts, but excluding net billed accounts receivable that collateralize the APP Facilities) plus (iii) investments with maturities of fewer than 12 months determined according to GAAP.

(iv)                              Section 6(1) of the Schedule to the Loan Agreement shall be amended by deleting the following text appearing at the end of the Section:

“; provided further, however, in all instances, Borrower shall not be required to deliver transaction reports to Bank during the period commencing August 1, 2007 through May 15, 2008.”

and inserting the following text in lieu thereof:

“; provided further, however, in all instances, Borrower shall not be required to deliver transaction reports to Bank during the period commencing August 1, 2007 through August 15, 2008.”

2

(v)                                 Section 6(2) of the Schedule to the Loan Agreement shall be amended by deleting the following text appearing at the end of the Section:

“; provided, however, Borrower shall not be required to deliver its monthly accounts payable agings to Bank during the period commencing November 1, 2007 through May 15, 2008.”

and inserting the following text in lieu thereof:

“; provided, however, Borrower shall not be required to deliver its monthly accounts payable agings to Bank during the period commencing November 1, 2007 through August 15, 2008 (reporting will be due as scheduled commencing with the period ending July 31, 2008).”

(vi)                              Section 6(3) of the Schedule to the Loan Agreement shall be amended by adding the following text at the end of the Section:

“; provided, however, Borrower shall not be required to deliver its monthly Receivable agings to Bank during the period commencing November 1, 2007 through May 15, 2008.”

and inserting the following text in lieu thereof:

“; provided, however, Borrower shall not be required to deliver its monthly Receivable agings to Bank during the period commencing November 1, 2007 through August 15, 2008 (reporting will be due as scheduled commencing with the period ending July 31, 2008).”

(vii)                           Section 6(4) of the Schedule to the Loan Agreement shall be amended by deleting the following text appearing at the end of the Section:

“; provided, however, Borrower may in lieu thereof deliver (i) its monthly unaudited financial statements for periods ending on a date between April 30, 2007 and July 31, 2007, inclusive, in draft form as soon as available, and in any event within thirty days after the end of each applicable month,  (ii) its monthly unaudited financial statement for period ending on August 31, 2007, in draft form as soon as available, and in any event on or before November 15, 2007,  (iii) its monthly unaudited financial statements for the period ending on September 30, 2007, in draft form as soon as available, and in any event no later than December 15, 2007,  (iv) its monthly unaudited financial statements for the period ending on December 31, 2007, in draft form as soon as available, and in any event no later than April 9, 2008, with final forms to be delivered to Bank within three days of the filing of such financial statements with the SEC but in no event later than May 15, 2008, and (v) its monthly unaudited financial statements for the period ending on March 31, 2008, as soon as available, and in any event no later than later than May 15, 2008.  Bank hereby waives (i) receipt of Borrower’s monthly unaudited financial statements for the periods ending October 31, 2007, November 30, 2007, January 31, 2008 and February 29, 2008 and (ii) receipt of Borrower’s monthly unaudited financial statement for the period ending December 31, 2007, in draft form, on or before January 31, 2008.”

“; provided, however, Borrower may in lieu thereof deliver (i) its monthly unaudited financial statements for periods ending on a date between April 30, 2007 and July 31, 2007, inclusive, in draft form as soon as available, and in any event within thirty days

3

after the end of each applicable month,  (ii) its monthly unaudited financial statement for period ending on August 31, 2007, in draft form as soon as available, and in any event on or before November 15, 2007, (iii) its monthly unaudited financial statements for the period ending on September 30, 2007, in draft form as soon as available, and in any event no later than December 15, 2007, (iv) its monthly unaudited financial statements for the period ending on December 31, 2007, in draft form as soon as available, and in any event no later than April 9, 2008, with final forms to be delivered to Bank within three days of the filing of such financial statements with the SEC but in no event later than July 15, 2008, and (v) its monthly unaudited financial statements for the period ending on March 31, 2008, in draft form as soon as available, and in any event no later than later than June 15, 2008, with final forms to be delivered to Bank within three days of the filing of such financial statements with the SEC but in no event later than July 15, 2008.  Bank hereby waives (i) receipt of Borrower’s monthly unaudited financial statements for the periods ending October 31, 2007, November 30, 2007, January 31, 2008, February 29, 2008, April 30, 2008 and May 31, 2008 and (ii) receipt of Borrower’s monthly unaudited financial statement for the period ending December 31, 2007, in draft form, on or before January 31, 2008.”

(viii)                        Section 6(5) of the Schedule to the Loan Agreement shall be amended by deleting the following text appearing at the end of the Section:

“; provided, however, (i) Borrower may in lieu thereof deliver its monthly Compliance Certificates for the period ending on a date between April 30, 2007 and November 30, 2007, inclusive, in draft form, provided further that Borrower delivers its monthly Compliance Certificates for the periods ending on June 30, 2007 and September 30, 2007 in final form, as soon as available, and in any event no later than May 15, 2008, (ii) Borrower may deliver its monthly Compliance Certificate for the period ending December 31, 2007, in draft form, as soon as available, and in any event no later than April 9, 2008, with final forms to be delivered to Bank as soon as available but in no event later than May 15, 2008, and (iii) Borrower may deliver its monthly Compliance Certificate for the period ending March 31, 2008, as soon as available, and in any event no later than May 15, 2008.  Bank hereby waives (i) receipt of Borrower’s monthly Compliance Certificates (i) for the periods ending October 31, 2007, November 30, 2007, January 31, 2008 and February 29, 2008 and (ii) receipt of Borrower’s monthly Compliance Certificate for the period ending December 31, 2007, in draft form, on or before January 31, 2008.”

and inserting the following text in lieu thereof:

“; provided, however, (i) Borrower may in lieu thereof deliver its monthly Compliance Certificates for the period ending on a date between April 30, 2007 and November 30, 2007, inclusive, in draft form, provided further that Borrower delivers its monthly Compliance Certificates for the periods ending on June 30, 2007 and September 30, 2007 in final form, as soon as available, and in any event no later than May 15, 2008, (ii) Borrower may deliver its monthly Compliance Certificate for the period ending December 31, 2007, in draft form, as soon as available, and in any event no later than April 9, 2008, with final forms to be delivered to Bank as soon as available but in no event later than July 15, 2008, and (iii) Borrower may deliver its monthly Compliance Certificate for the period ending March 31, 2008, in draft form, as soon as available, and in any event no later than June 15, 2008, with final forms to be delivered to Bank as soon as available but in no event later than July 15, 2008.  Bank hereby waives (i) receipt of Borrower’s monthly Compliance Certificates (x) for the periods ending October 31, 2007, November 30, 2007, January 31, 2008, February 29, 2008, April 30, 2008 and May

4

31, 2008 and (y) receipt of Borrower’s monthly Compliance Certificate for the period ending December 31, 2007, in draft form, on or before January 31, 2008.”

(ix)                                Section 6(6) of the Schedule to the Loan Agreement shall be amended by deleting the following text appearing at the end of the Section:

“; provided, however, Borrower may in lieu thereof deliver its quarterly unaudited financial statements for the periods ending on June 30, 2007, September 30, 2007 and December 31, 2007 in draft form as soon as available, and in any event no later than April 9, 2008, with final forms of the September 30, 2007 and December 31, 2007 quarterly unaudited financial statements to be delivered to Bank within three days of the filing of such financial statements with the SEC but in no event later than May 15, 2008.  Bank hereby waives receipt of Borrower’s quarterly unaudited financial statement for the period ending December 31, 2007 in draft form on or before February 15, 2008.”

and inserting the following text in lieu thereof:

“; provided, however, Borrower may in lieu thereof (i) deliver its quarterly unaudited financial statements for the periods ending on June 30, 2007, September 30, 2007 and December 31, 2007 in draft form as soon as available, and in any event no later than April 9, 2008, with final forms of the September 30, 2007 quarterly unaudited financial statements to be delivered to Bank within three days of the filing of such financial statements with the SEC but in no event later than May 15, 2008; (ii) deliver its quarterly unaudited financial statements for the period ending on December 31, 2007 in final form within three days of the filing of such financial statements with the SEC but in no event later than July 15, 2008; and (iii) deliver its quarterly unaudited financial statements for the period ending on March 31, 2008 in draft form as soon as available, and in any event no later than June 15, 2008, with final forms of the March 31, 2008 quarterly unaudited financial statements to be delivered to Bank within three days of the filing of such financial statements with the SEC but in no event later than July 15, 2008.  Bank hereby waives receipt of Borrower’s quarterly unaudited financial statement for the period ending December 31, 2007 in draft form on or before February 15, 2008.”

(x)                                   Section 6(7) of the Schedule to the Loan Agreement shall be amended by adding the following text at the end of the Section:

“; provided, further, that Borrower may deliver its annual operating budgets (including income statements, by quarter) for its fiscal year end 2009 on or before June 15, 2008.    Bank hereby waives receipt of Borrower’s pro forma balance sheet and pro forma statement of cash flows for its fiscal year end 2009. ”

4.                                       FEES.  Borrower shall pay to Bank a modification fee of One Hundred Twenty Five Thousand Dollars ($125,000), which fee shall be due on the date hereof and shall be deemed fully earned as of the date hereof.  Borrower shall also reimburse Bank for all legal fees and expenses incurred in connection with this amendment to the Existing Loan Documents.

5.                                       RATIFICATION OF NEGATIVE PLEDGE.  Borrower hereby ratifies, confirms and reaffirms, all and singular, the terms and conditions of a certain Negative Pledge Agreements each dated as of January 30, 2003 between Borrower and Bank, and acknowledges, confirms and agrees that said Negative Pledge Agreement shall remain in full force and effect.

6.                                       RATIFICATION OF PERFECTION CERTIFICATES.  Borrower hereby ratifies, confirms and reaffirms, all and singular, the terms and disclosures contained in certain Perfection Certificates each

5

dated as of January 30, 2003, as amended and affected by Schedule 1 to the Fourth Amendment and Exhibit A to the Fourth Amendment and acknowledges, confirms and agrees the disclosures and information therein, in Schedule 3.10 to the Loan Agreement, in Schedule 1 annexed to the Tenth Loan Modification Agreement, and/or in connection with the formation of subsidiaries as contemplated by the Guggenheim Transactions and the Key Transactions (as defined in the Sixth Loan Modification Agreement and the Eleventh Loan Modification Agreement, respectively), have not changed as of the date hereof.

7.                                       CONSISTENT CHANGES.  The Existing Loan Documents are hereby amended wherever necessary to reflect the changes described above.

8.                                       RATIFICATION OF LOAN DOCUMENTS.  Borrower hereby ratifies, confirms, and reaffirms all terms and conditions of all security or other collateral granted to the Bank and confirms that the indebtedness secured thereby includes, without limitation, the Obligations.

9.                                       NO DEFENSES OF BORROWER.  Borrower hereby acknowledges and agrees that Borrower has no offsets, defenses, claims, or counterclaims against Bank with respect to the Obligations, or otherwise, and that if Borrower now has, or ever did have, any offsets, defenses, claims, or counterclaims against Bank, whether known or unknown, at law or in equity, all of them are hereby expressly WAIVED and Borrower hereby RELEASES Bank from any liability thereunder.

10.                                 CONTINUING VALIDITY.  Borrower understands and agrees that in modifying the existing Obligations, Bank is relying upon Borrower’s representations, warranties, and agreements, as set forth in the Existing Loan Documents, after giving effect to this Loan Modification Agreement and the Waiver Agreement entered into between Borrower and Bank dated as of the date hereof.  Except as expressly modified pursuant to this Loan Modification Agreement, the terms of the Existing Loan Documents remain unchanged and in full force and effect.  Bank’s agreement to modifications to the existing Obligations pursuant to this Loan Modification Agreement in no way shall obligate Bank to make any future modifications to the Obligations.  Nothing in this Loan Modification Agreement shall constitute a satisfaction of the Obligations.  It is the intention of Bank and Borrower to retain as liable parties all makers of Existing Loan Documents, unless the party is expressly released by Bank in writing.

11.                                 COUNTERSIGNATURE.  This Loan Modification Agreement shall become effective only when it shall have been executed by Borrower and Bank.

[Remainder of page intentionally left blank.]

6

This Loan Modification Agreement is executed as a sealed instrument under the laws of the Commonwealth of Massachusetts as of the date first written above.

The undersigned, ASPENTECH SECURITIES CORP., a Massachusetts corporation,  ratifies, confirms and reaffirms, all and singular, the terms and conditions of a certain Unlimited Guaranty dated January 30, 2003 (the “Guaranty”) and a certain Security Agreement dated as of January 30, 2003 (the “Security Agreement”) and acknowledges, confirms and agrees that the Guaranty and Security Agreement shall remain in full force and effect and shall in no way be limited by the execution of this Loan Modification Agreement, or any other documents, instruments and/or agreements executed and/or delivered in connection herewith.