The Senate, by a vote of 58 to 42, yesterday rejected President Reagan's nomination of Judge Robert H. Bork to the Supreme Court, climaxing a fierce 3 1/2-month struggle that polarized the Senate and inflamed political passions across the country.

The number of votes against the nomination and the margin of defeat were the largest for any Supreme Court nominee in history.

Senate Democrats immediately called on Reagan not to follow through on his vow to propose another nominee that senators will "object to as much as they did to this one."

"It is time to start the healing," Senate Majority Leader Robert C. Byrd (D-W.Va.) said. "I urge the president to back away from a policy of defiance. I urge that we all back away from a policy of defiance."

Senate Judiciary Committee Chairman Joseph R. Biden Jr. (D-Del.) said he, Byrd and Republican leaders will meet with White House chief of staff Howard H. Baker Jr. early next week to discuss the next nominee.

"If he {Reagan} sends someone up who has the same views {as Bork}, I believe he will not only have trouble, he will not have a nominee," Biden said.

The president met with Attorney General Edwin Meese III yesterday to discuss the next nomination, but Justice Department spokesman Terry H. Eastland said he did not know whether specific names were discussed. He said he expects a new nominee "toward the end of next week," after Meese has returned from services in San Diego for his young grandson, who died this week.

In a statement issued by the White House, Reagan said his next nominee "will share Judge Bork's belief in judicial restraint -- that a judge is bound by the Constitution to interpret the laws, not make them."

The president said he was "saddened and disappointed that the Senate has bowed today to a campaign of political pressure," adding: "In the last few months, the confirmation of a judicial nominee has become a spectacle of misrepresentation and single-issue politics. To allow this unprecedented practice to become the rule would jeopardize the integrity and independence of the American system of justice."

Federal appeals court Judges Pasco M. Bowman II of Kansas City and Anthony M. Kennedy of Sacramento are leading contenders for the nomination, Justice Department sources said. Appeals court Judges Laurence Silberman and Douglas H. Ginsburg of the District and Ralph K. Winter of New Haven, Conn., are also high on the list.

J. Clifford Wallace of San Diego, Roger J. Miner of Albany, N.Y., and Edith H. Jones of Houston are also under consideration, according to the sources.

Two other appelate judges, William W. Wilkins Jr. of Greenville, S.C., a favorite of Sen. Strom Thurmond (R-S.C.), and Patrick E. Higginbotham of Dallas, mentioned as a candidate by several southern Democrats who opposed Bork, are also on the short list, the sources said, but there is little support for them.

The list of prospective names has been reviewed by Meese, Assistant Attorney General William Bradford Reynolds, Baker, White House Counsel A.B. Culvahouse and deputy White House chief of staff Kenneth M. Duberstein, a White House official said.

Biden said there is "no possibility" that a new nominee could be confirmed before Thanksgiving and that confirmation this year would depend on Congress' adjournment date. Congress has set a tentative adjournment date of Nov. 21, but that is widely expected to slip because of the backlog of legislative business.

As the Senate voted, Bork was eating lunch in the Montpelier Room of the Madison Hotel in downtown Washington. He refused to comment on his defeat, but in a statement issued from his chambers at the Court of Appeals here, he said that "although not all the voices were lowered as I had hoped, I am, nevertheless, glad the debate took place.

"There is now a full and permanent record by which the future may judge not only me but the proper nature of a confirmation proceeding," he continued. "A time will come when I will speak to the question of the process due in these matters, but that time is not now."

Six Republicans joined 52 Democrats in opposing confirmation. Sens. David L. Boren (D-Okla.) and Ernest F. Hollings (D-S.C.) were the only Democrats to support Bork. Sens. John W. Warner (R-Va.), William Proxmire (D-Wis.) and John C. Stennis (D-Miss.) -- the only senators who were not publicly committed -- each voted against confirmation.

Of the 10 senators who were publicly uncommitted on Oct. 9 when Bork, in the face of almost certain defeat, demanded a debate and vote on the nomination by the full Senate, five voted for confirmation and five against.

Although Bork has been seen as defeated for three weeks, yesterday's 16-minute roll call took place in a solemn, ritualized atmosphere after Byrd requested that senators stand at their desks to vote rather than mill around talking on the floor.

Bork's wife, Mary Ellen, and his sons, Robert Jr. and Charles, watched portions of the final hours of the debate from the Senate visitors' gallery, but they were not present for the roll call.

After the vote, Biden walked over to Thurmond, the Judiciary Committee's ranking Republican, and shook hands with him.

Thurmond said later he expected Reagan to nominate a conservative who is "not so controversial" as Bork. Urging the president to choose a southerner, he added, "I think the next candidate will be confirmed shortly."

The 58 votes against Bork exceeded the 55 cast against President Richard M. Nixon's nomination of Clement F. Haynsworth in 1969. The 16-vote margin exceeded the Senate's 24-to-9 rejection of Alexander Wolcott, nominated to the Supreme Court in 1811 by President James Madison.

Bork was the 27th nominee to the high court to be denied confirmation and the 12th to be rejected outright.

Reagan nominated Bork, 60, a former Yale Law School professor and Court of Appeals judge here since 1982, on July 1 to succeed Justice Lewis F. Powell Jr., who retired. The nomination set off an intense struggle, including a public campaign to defeat the nomination that became the focal point of the Senate debate in the closing days of the battle.

"We will look back in embarrassment that we rejected such a remarkable man who who could have injected such yeast into the court," said Minority Whip Alan K. Simpson (R-Wyo.).

But Democrats said that pressure tactics were used by both sides in the lengthy fight and that Bork was given every opportunity to explain his views. Byrd noted that he and three other Judiciary Committee members, including Republican Sen. Arlen Specter (R-Pa.), began the hearings undecided and that all four voted against confirmation.

"We were open to persuasion," he said. "We were not persuaded. We were unsettled by Judge Bork's overly narrow interpretation of the law. That feeling of unease reflected the unease of the American people that Judge Bork would not protect their rights."

If Bowman is nominated, he is sure to be questioned about his tenure as dean of the Wake Forest University law school in Winston-Salem, N.C.

Officials at Wake Forest said Bowman was asked to leave in 1978 after a dispute over a labor law institute that he established under the leadership of Sylvester Petro, who taught Bowman labor law while he was a law student at New York University.

The institute, the Wake Forest Institute for Labor Policy Analysis, was seen as antiunion in its orientation, according to former university president James Ralph Scales.

He was later dean of the law school at the University of Missouri in Kansas City before being named to the 8th U.S. Circuit Court of Appeals by Reagan in 1983. Bowman is a close political ally of Sen. Jesse Helms (R-N.C.), who strongly supported him for the appeals court.

Kennedy, 51, appointed to the 9th U.S. Circuit Court of Appeals by President Gerald R. Ford in 1976, wrote the appeals court decision in Chadha v. Immigration and Naturalization Service, holding that the one-house "legislative veto" violated the constitutional doctrine of separation of powers. The Supreme Court later upheld that ruling.