She was launched on 7 December 1968, sponsored by Mrs. Charles F. Baird, wife of the Under Secretary of the Navy, and commissioned on 4 February 1970.

"[4] On 2 October 1975, Chief of Naval Operations Admiral James L. Holloway III found the captain of Finback "guilty of permitting an action, which could have distracted the attention of those responsible for the safe navigation of the nuclear-powered submarine maneuvering in restricted waters."

Holloway agreed with subordinates that the captain had failed to exercise good judgement and did not follow the regulations governing civilian visitors to naval vessels.

In 1986, Finback won the Marjorie Sterrett Battleship Fund Award for the United States Atlantic Fleet.

Her scrapping via the Nuclear-Powered Ship and Submarine Recycling Program at Puget Sound Naval Shipyard in Bremerton, Washington, was completed on 30 October 1997.