Cyrus R. Vance, the next Secretary of State, comes from one of New York's largest, oldest and most influential law firms, Simpson, Thatcher & Bartlett.

The firm was founded in 1884, and has always included prominent citizens, including many who served in the government. Its senior partner today is Whitney North Seymour, 76, father of the former U.S. attorney who prosecuted Watergate defendants John Mitchell and Maurice Stans, and one of the most respected lawyers in New York.

Simpson, Thatcher now has about 160 lawyer, engaged primarily in securities law, wills, corporate advice and all types of civil litigation. In an interview, Seymour said the firm practically never does criminal work.

Clients include Manufacturers' Hanover Trust Co., Gulf & Western, American Electric Power, Lehman Brothers, Loeb Rhodes & Co. and Pan American World Airways. A partner in another big New York firm described Simpson, Thatcher as "the best on Wall Street. I've never heard anybody say anything negative about this outfit."

Gulf & Western is said to be the biggest single client, and it was also the source of the biggest scandal in the law firm's history. In September, 1974, the firm fired a partner, Joel Doikart, who also sat on Gulf & Western's board - from which he was also fired. This followed the disappearance of $1.5 million in fees Gulf & Western had paid to the firm.

It was an embarrassing scandal but, according to numerous sources here, Simpson, Thatcher handled it with dignity and candor.

The firm had permitted Vance to engage in a lot of outside activities, some on behalf of corporations, many for non-profit causes. Vance has done litigation work in the firm for clients like Lehman Brothers and G.A.F. Corp., reportedly earning about $250,000 yearly.

He has also been a director of IBM, Pan Am, New York Times Co. and others. And he has been a trustee of the Rockefeller Foundation, Columbia Presbyterian Hospital, the Urban Institute and Yale.

In 1971 Vance helped set up the Knapp Commission, which investigated police corruption in New York. He was an active president of the New York Bar Association, involved in human rights causes, legal representation for the poor and other volunteer efforts. During New York's financial crisis he was a volunteer adviser to city and state officials. He has long been active in foreign policy organizations.

Vance plans to remain on the Yale Corporation, but has already begun to resign from his other boards, including the corporate ones. (He quit Pan Am early in December.) Seymour said the separation from the firm will be complete and entirely proper.