Exhibit (e)(6)

VIGOR INDUSTRIAL LLC

5555 N. Channel Ave.

Portland, OR 97217

November 6, 2010

CONFIDENTIAL

Mr. Patrick W.E. Hodgson

Chairman of the Transaction Committee

Todd Shipyards Corporation

1801 16^th Ave. SW

Seattle, WA 98134-1017

Dear Mr. Hodgson:

In connection with the discussions of a potential transaction (the “Transaction”) in which Vigor Industrial LLC (“Parent”) would purchase Todd Shipyards Corporation (the “Company”), the Company has agreed to enter into this letter agreement and to be bound in accordance with the terms hereof.

The Company agrees, for a period beginning on the date of this letter and ending on the earlier to occur of (i) November 30, 2010 and (ii) the execution and delivery of a definitive merger agreement, that it will not, directly or indirectly, solicit or facilitate, or participate in any discussions or negotiations (including by way of providing information) with, any other person that has made or, to the Company’s knowledge, is considering making, a proposal with respect to the acquisition of 10% or more of the equity interests, assets, net revenues or net income of the Company (whether through a merger, acquisition, reorganization, recapitalization, dissolution tender offer, joint venture or other transaction).

All fees and expenses incurred by each party hereto in connection with the preparation of this letter agreement shall be borne by such party.

The Confidentiality Agreement previously executed by the parties shall remain in full force and effect. In addition, the parties agree to not disclose the existence or the provisions of this letter agreement or any term sheet executed by the Company and Parent to any person, except for its employees and advisors who need to know of such terms in order to facilitate the closing of the Transaction, each of whom shall be informed of the confidential nature of such term sheet, this letter agreement and the Transaction. Upon execution of a definitive merger agreement, the parties shall cooperate in issuing a mutually agreeable press release regarding the Transaction.

This letter agreement shall be governed by the laws of State of Delaware, without regard to conflict of laws provisions. This letter agreement may be executed in counterparts, each of which shall be deemed an original. The delivery of an executed counterpart of this letter agreement by facsimile or e-mail shall be deemed to be an original.

No legally binding obligation or commitment with respect to a Transaction will be created, implied or inferred until the execution and delivery of definitive agreements containing the more definitive and detailed terms of the Transaction that have been approved by the Board of Directors of the Company or a duly formed Transaction Committee of such Board and the Board of Managers and the majority member of Vigor Industrial LLC.

Please indicate your acknowledgement and agreement with the terms of this letter agreement by signing below.

Sincerely,

VIGOR INDUSTRIAL LLC

/s/ Frank Foti

Frank Foti

President and CEO

Accepted and agreed this 12^th day of November 2010 by:

TODD SHIPYARDS CORPORATION

/s/ Patrick W.E. Hodgson

Patrick W.E. Hodgson

Chairman of the Transaction Committee