Exhibit 10.35

SEVERANCE AGREEMENT

THIS AGREEMENT is entered into as of May 22, 2006 by and between Eric Schwartz (the “Executive”) and EQUINIX, INC., a Delaware corporation (the “Company”).

This Agreement shall remain in effect from the date hereof until the earlier of:

(a) The date the Executive’s employment with the Company terminates for a reason other than a Qualifying Termination as described in Section 4(d); or

(b) The date the Company has met all of its obligations under this Agreement following a termination of the Executive’s employment with the Company for a reason described in Section 4(d).

(a) Severance Benefit. If the Executive is subject to a Qualifying Termination, then the Company shall pay the Executive 100% of his or her annual base salary and target bonus (at the annual rate in effect at the time of the Qualifying Termination). Such severance benefit shall be paid in accordance with the Company’s standard payroll procedures. The Executive will receive his or her severance payment in a cash lump-sum which will be made within ten (10) business days of the latest of the following dates:

(i) the date of Executive’s Qualifying Termination;

(ii) the date of the Company’s receipt of the Executive’s executed General Release; and

(iii) the expiration of any rescission period applicable to the Executive’s executed General Release.

(b) Health Care Benefit. If the Executive is subject to a Qualifying Termination, and if the Executive elects to continue his or her health insurance coverage under the Consolidated Omnibus Budget Reconciliation Act (“COBRA”) following the termination of his or her employment, then the Company shall pay the Executive’s monthly premium under COBRA until the earliest of (i) the close of the twelve-month period following cessation of his or her employment or (ii) the expiration of the Executive’s continuation coverage under COBRA.

(c) General Release. Any other provision of this Agreement notwithstanding, Subsections (a) and (b) above shall not apply unless the Executive (i) has executed a general release (in a form prescribed by the Company) of all known and unknown claims that he or she may then have against the Company or persons affiliated with the Company and (ii) has agreed not to prosecute any legal action or other proceeding based upon any of such claims.

(d) The other provisions of Sections 2(a) and (b) above notwithstanding, the payment(s) under Section 2(a) and the COBRA reimbursements under Section 2(b) shall in no event commence prior to the earliest date permitted by section 409A(a)(2) of the Internal Revenue Code of 1986, as amended (“the Code”). If the commencement of such payments or reimbursements must be delayed, then any deferred installments shall be paid in a lump sum on the earliest practicable date permitted by section 409A(a)(2) of the Code.

(a) Non-Solicitation. During the Executive’s employment with the Company and during the twelve-month period following his or her cessation of employment, the Executive shall not directly or indirectly, personally or through others, solicit or attempt to solicit the employment of any employee of the Company or any of the Company’s affiliates, whether on the Executive’s own behalf or on behalf of any other person or entity. The Executive and the Company agree that this provision is reasonably enforced as to any geographic area in which the Company conducts its business.

(b) Non-Competition. The Executive agrees that, during his or her employment with the Company, he or she shall not engage in any other employment, consulting or other business activity (whether full-time or part-time) that would create a conflict of interest with the Company.

(c) Cooperation and Non-Disparagement. The Executive agrees that, during the twelve-month period following his or her cessation of employment, he or she shall cooperate with the Company in every reasonable respect and shall use his or her best efforts to assist the Company with the transition of Executive’s duties to his or her successor. The Executive further agrees that, during this twelve-month period, he or she shall not in any way or by any means disparage the Company, the members of the Company’s Board of Directors or the Company’s officers and employees.

(a) Definition of “Cause.” For all purposes under this Agreement, “Cause” shall mean the Executive’s unauthorized use or disclosure of trade secrets which causes material harm to the Company, the Executive’s conviction of, or a plea of “guilty” or “no contest” to, a felony, or the Executive’s gross misconduct. The foregoing shall not be deemed an exclusive list of all acts or omissions that the Company may consider as grounds for the termination of the Executive’s employment without Cause.

(b) Definition of “Change in Control.” For all purposes under this Agreement, “Change in Control” shall have the meaning ascribed to such term in Section 19.4 of the Company’s 2000 Equity Incentive Plan.

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(c) Definition of “Good Reason.” For all purposes under this Agreement, “Good Reason” shall mean (i) a change in the Executive’s position with the Company that materially reduces his or her authority or level of responsibility, (ii) a reduction in his or her level of compensation (including base salary and target bonus) other than pursuant to a reduction of compensation for other executive employees of the Company, or (iii) a relocation of his or her place of employment by more than 30 miles, provided and only if such change, reduction or relocation is effected by the Company without his or her consent.

(d) Definition of “Qualifying Termination.” For all purposes under this Agreement, “Qualifying Termination” shall mean that one of the following events occurs within 18 months after a Change in Control of the Company:

(i) The Executive voluntarily resigns his or her employment for Good Reason; or

(ii) The Company terminates the Executive’s employment for any reason other than Cause.

(a) Company’s Successors. The Company shall require any successor (whether direct or indirect and whether by purchase, lease, merger, consolidation, liquidation or otherwise) to all or substantially all of the Company’s business and/or assets, by an agreement in substance and form satisfactory to the Executive, to assume this Agreement and to agree expressly to perform this Agreement in the same manner and to the same extent as the Company would be required to perform it in the absence of a succession. For all purposes under this Agreement, the term “Company” shall include any successor to the Company’s business and/or assets or which becomes bound by this Agreement by operation of law.

(b) Executive’s Successors. This Agreement and all rights of the Executive hereunder shall inure to the benefit of, and be enforceable by, the Executive’s personal or legal representatives, executors, administrators, successors, heirs, distributees, devisees and legatees.

(a) Other Severance Arrangements. This Agreement supersedes any and all cash severance arrangements on change in control under any prior separation, severance and salary continuation arrangements, programs and plans which were previously offered by the Company to the Executive, including change in control severance arrangements pursuant to an employment agreement or offer letter. In no event shall any individual receive cash severance benefits under both this Agreement and any other severance pay or salary continuation program, plan or other arrangement with the Company.

(b) Notice. Notices and all other communications contemplated by this Agreement shall be in writing and shall be deemed to have been duly given when personally delivered or when mailed by U.S. registered or certified mail, return receipt requested and

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postage prepaid or deposited with Federal Express Corporation, with shipping charges prepaid. In the case of the Executive, mailed notices shall be addressed to him or her at the home address which he or she most recently communicated to the Company in writing. In the case of the Company, mailed notices shall be addressed to its corporate headquarters, and all notices shall be directed to the attention of its Secretary.

(c) Waiver. No provision of this Agreement shall be modified, waived or discharged unless the modification, waiver or discharge is agreed to in writing and signed by the Executive and by an authorized officer of the Company (other than the Executive). No waiver by either party of any breach of, or of compliance with, any condition or provision of this Agreement by the other party shall be considered a waiver of any other condition or provision or of the same condition or provision at another time.

(d) Withholding Taxes. All payments made under this Agreement shall be subject to reduction to reflect taxes or other charges required to be withheld by law.

(e) Severability. The invalidity or unenforceability of any provision or provisions of this Agreement shall not affect the validity or enforceability of any other provision hereof, which shall remain in full force and effect.

(f) No Retention Rights. Nothing in this Agreement shall confer upon the Executive any right to continue in service for any period of specific duration or interfere with or otherwise restrict in any way the rights of the Company or any subsidiary of the Company or of the Executive, which rights are hereby expressly reserved by each, to terminate his or her service at any time and for any reason, with or without Cause.

(g) Choice of Law. The validity, interpretation, construction and performance of this Agreement shall be governed by the laws of the State of California (other than their choice-of-law provisions).

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IN WITNESS WHEREOF, each of the parties has executed this Agreement, in the case of the Company by its duly authorized officer, as of the day and year first above written.

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