Two leading contenders to succeed Virginia's Harry F. Byrd Jr. in the U.S. Senate -- Rep. Stanford Parris (R-Va.) and former Democratic Sen. William B. Spong Jr. -- have dropped out of the race, increasing the pressure on a field of undecideds to declare their candidacies.

More announcements in the 1982 Senate contest are expected in the next few weeks, as both parties reassemble their forces for the first statewide rematch since last November's sweeping Democratic victories.

Parris' announcement yesterday that he will seek reelection to his Northern Virginia congressional seat narrowed the top Republican choices for the Senate and clears the way for a consensus GOP candidate in next year's election to replace Byrd, the conservative independent who announced he will not seek another term.

The leading Republican now is Rep. Paul S. Trible (R-Va.), who has recently picked up some support from a key conservative faction in Richmond. Trible's main threat for the nomination appears to be Wyatt B. Durrette, a former candidate for state attorney general who is expected to announce his intentions today or tomorrow.

Spong, the last Virginia Democrat to be elected to the Senate, said during the weekend that he won't run for his old job in 1982. Spong, now dean of the Marshall-Wythe School of Law at The College of William and Mary, told a Richmond newspaper he believes the Democrats need "a candidate whose appetite for public office is greater than mine." He also said he would not be a candidate for an upcoming vacancy on the Virginia Supreme Court.

Spong, who was defeated for reelection to the Senate in 1972, was the clear favorite of Democratic party regulars in a recent straw poll, but a number of other Democratic candidates have been mentioned. Former state attorney general Andrew P. Miller, another likely Democratic contender, said yesterday he will announce his plans early next month, as did the state party chairman, Del. Owen Pickett (D-Virginia Beach).

As the Senate race begins to shape up, Republicans are stressing party unity, hoping to avoid needless bloodletting at the nominating convention in Richmond next June. Democrats will choose their candidates at a summer convention in Roanoke.

A new element in the Senate race is the departure of actress Elizabeth Taylor from the Virginia political scene. The wife of Sen. John Warner (R-Va.), who announced the couple's separation yesterday, has been a formidable drawing card at Republican fund-raisers in recent years.

After three weeks of probing the depth of his statewide support, Parris yesterday withdrew his name from the Senate race and announced he will seek reelection. His main concern, he said, was to "finish the tasks the people of the 8th Congressional District assigned to me" and to block the resurgence of his old foe, Democrat Herbert E. Harris.

"I would be content with an epitaph saying I'm the guy who permanently retired Herb Harris from public office," said Parris at a Capitol Hill news conference. The rivalry between Parris and Harris dates to 1974 when Harris unseated Parris; in 1980 Parris drove Harris from office.

Parris' candidacy for the Senate had been touted by certain Republican leaders who were reluctant to concede the party's nomination to 34-year-old Trible, whose youth and ambition reminded them of J. Marshall Coleman, the GOP's unsuccessful 1981 gubernatorial candidate. According to party officials, many of those same leaders have also turned to Durrette who, in spite of his defeat at the polls last November, is still a favorite among Virginia's conservative coalition. D. French Slaughter Jr., a former delegate from Culpeper, has also been checking with supporters about a possible Senate run, but he is not well known to Virginia voters.

Durrette has made no secret of his reluctance for another costly, time-consuming campaign and has said he would run only out of a sense of "responsibility for my party and my principles."

He said he was finding more support for Trible among party leaders than his own boosters suspected. Last week, Trible announced the formation of a 20-member campaign committee, including five GOP district chairmen and Rep. G. William Whitehurst (R-Va.).

Since then, Trible has picked up support from James Wheat of Richmond's Wheat First Securities, a staunch conservative of the so-called "Main Street" faction, who has sent out a letter on Trible's behalf, according to party officials.

Parris, who kept his own staff guessing on his decision until early yesterday, said he was confident he could have raised enough money for a multimillion-dollar Senate race and that he could win both the GOP nomination next summer and the general election in the fall.

Despite these convictions, Parris said he agonized over the decision, secluding himself in a cabin in the Blue Ridge mountains last weekend while he continued a round of phone calls and studied polls produced by his staff. In the end, he said the decision was an extremely close call, close enough for him to ask his staff to prepare two different statements for yesterday's press conference.

Parris' decision was greeted warmly yesterday by Democrat Harris, who will also be announcing his plans next month: "I sympathize with Stan because he was apparently rejected by the Republican leadership in the state, but I'm not so sure the people in the 8th District are anxious to have him come back there either."