President Reagan yesterday appointed four new men to the board of the Legal Services Corp. By making the appointments with Congress out of session, the appointees will be able to serve through 1984 without Senate confirmation.

The nominees are a Washington lawyer, an Arizona business executive, the dean of the New York Law School and a San Francisco lawyer.

Legal Services advocates reacted cautiously to word of the nominees, who are not widely known in Washington, but criticized the recess nomination process.

Clint Lyons, the former acting president of the Legal Services Corp., said, "It is a tragedy that the manipulation of the recess appointment process has resulted in a situation where two years into the administration, there is still not an 11-member board confirmed by the Senate."

Yesterday's nominations mark the second time Reagan has made recess appointments to the board. Most of the members of the last board were formally nominated and sent up for Senate confirmation after Reagan named them as recess appointees.

But when the president received word that two of his nominees would be rejected by the Senate, he withdrew all the names. Their recess appointments expired last month when Congress adjourned.

There was no word from the White House on whether Reagan intends to make additional nominations to the 11-member board or whether he will submit these names or any others for Senate confirmation. The board could operate legally under District of Columbia law with as few as four members.

Two members of the previous board, Washington lawyer Frank Donatelli and Dan Rathbun, a Virginia college student, were not appointed until last October and can continue to serve until the end of this year.

Unless the new board members are formally nominated and approved by Congress, they will be largely restrained in the kind of impact they can have on Legal Services.

Before it adjourned last month, Congress attached to government funding legislation a rider that prohibits an unconfirmed board from cutting back existing programs to provide free legal assistance to the poor.

Reagan has twice tried unsuccessfully to eliminate all funding for the program. Congress did not go along with his plans but did vote two years ago to cut the budget by 25 percent, where it has stayed since. Reagan is expected to propose a zero budget for Legal Services in his 1984 budget.

The new appointees:

Milton M. Masson, 41, a member of the U.S. Synfuels Corp., executive vice president and treasurer of Sullivan and Masson Inc., a firm of consulting engineers, architects and construction managers based in Arizona. He is also vice president and a board member of Sun Eagle Development Co. in Colorado.

Robert E. McCarthy, 62, a senior partner with the San Francisco law firm of Bohnert, McCarthy, Flowers, Roberts and Damir. He served as a consultant to the White House Office of Policy Development in 1981 and 1982.

Donald E. Santarelli, 45, of Alexandria, a lawyer with the Washington, D.C., firm of Santarelli and Gimer. He is a board member of the Overseas Private Investment Corp. He was a lawyer in the Justice Department in the Nixon administration and is a former head of the Law Enforcement Assistance Administration.

E. Donald Shapiro, 51, dean and a professor of law at the New York Law School. He lives in Short Hills, N.J.