Democrats from across Virginia entered the U.S. Senate race yesterday, offering themselves as "favorite sons" for a nomination that appeared more wide open than ever after another leading party figure withdrew from consideration.

Senate Majority Leader Hunter B. Andrews of Hampton, considered briefly the front-runner in the Democrats' chaotic scramble for a Senate candidate, bowed out of the race, citing the difficulties of raising money and putting together a statewide campaign at this late date. The Democrats will nominate their candidate in Roanoke on June 5.

Within hours of Andrews' statement, campaigns sprouted all over the state--pushing former congressman Joseph L. Fisher and Fairfax prosecutor Robert F. Horan in Northern Virginia, state Sen. Virgil Goode in the state's southwestern corner and Del. Norman Sisisky, a wealthy beer distributor from Petersburg.

Both Horan, who has declared himself a candidate, and Fisher, who has stopped just short of that, appeared before a meeting of 10th District nominating convention delegates last night where each called for a campaign focusing on failures of the Republican administration.

After a lengthy and sometimes divisive debate, the delegation--which represents all of Arlington and parts of Fairfax County--adopted a resolution that urged Fisher to run and at the same time "applauded" Horan's entry into the race.

The resolution did nothing to dispel fears of some local Democrats who are concerned that two Northern Virginia candidates would dilute the region's voting strength in Roanoke.

"I hope Bob and Joe don't slug it out," said l0th District Chairman Mary Cahill.

The sudden burst of regional candidacies--some declared, some considered imminent--increased the possibility of a brokered Democratic convention, a prospect that some party members fear will leave the party divided in the fall campaign against congressman Paul S. Trible of Newport News, who is unopposed for the Republican nomination.

"As far as the party leadership is concerned, this is a do-or-die situation," said former attorney general Andrew Miller, the unsuccessful Democratic nominee for the Senate in 1978, who still has an interest in the nomination this year.

"This is appalling," said one party official, who asked not to be named. "The party is in total disarray."

Andrews, a powerful figure in the state legislature and one of the party's most forceful orators, is the third leading candidate to take himself out of Senate race. The first, state delegate and former party chairman Owen B. Pickett, withdrew several weeks ago to head off the threat of an independent campaign by Virginia's top-ranking black officeholder, state Sen. L. Douglas Wilder of Richmond.

Last week Lt. Gov. Richard J. Davis, the Democrats' top vote getter last fall and a clear favorite of party officials for the nomination, also said he would not run this year, saying his current duties would prevent him from engaging in an all-out statewide campaign.

In a statement issued through Senate clerk J.T. Shropshire yesterday, Andrews said he decided against seeking the nomination because of "the problems of necessary funding and organization within the preconvention period."

Gov. Charles S. Robb yesterday greeted Andrews' announcment with regret. The governor said he was "disappointed when one of Virginia's most talented legislative leaders and debaters . . . decides not to become a candidate."

However, according to one Democrat, Robb was privately less than encouraging about an Andrews campaign when the two met at a Norfolk hotel a week and a half ago. That conversation, while not the determining factor in his decision, wounded Andrews' pride, according to the official. Andrews' decision leaves the Democrats without a candidate who would be able to walk into the convention with a majority of the party's 3,624 delegates. "No one will have a majority, which means there will have to be some trading back and forth," said 3rd District party chairman Angus MacAuley of Richmond. "It will be very interesting."

Fairfax prosecutor Horan declared himself a Senate candidate over the weekend, although he said a formal announcement would not be made until tomorrow. Horan said he was less concerned than some of the other potential candidates with the difficulty they all face in raising money. "A lot of good Democrats opted not to run because of the money," he said. "I just decided 'to heck with the money--let's go.' "

Fisher, now a member of Robb's cabinet, decided to explore a Senate race after a May 15 meeting in Fredericksburg with political advisers John Milliken, a member of the Arlington County Board, and Lucy Denny, an Arlington activist. "As far as we are concerned, if he is nominated, he will run," Denny said yesterday, "He will have his name put in nomination at the convention."

Fisher, 67, who lost his last race for Congress against Rep. Frank Wolf, said before the meeting last night that he was calling friends with this message: "If you want me to run, say so, why, how much and how badly."

Goode, 35, now serving his second term in the Senate, entered the race claiming he would offer "a voice speaking for the average citizen." Regarded as a moderate-liberal in the state Senate, Goode has cultivated a populist image, leading fights against the state's public utilities and big business.

Sisisky, who operates a beer and soft drink distributorship in Petersburg, has been mentioned as a darkhorse candidate by party officials for several weeks, largely because of his reported ability to donate as much as $500,000 to his own campaign. Tom King, Sisisky's campaign manager in the 4th District congressional race, said yesterday an announcement could be expected sometime today. "We're not going to pussyfoot around," King said. "If we decide to go for it, we'll go and make an all-out bid."

Other candidates mentioned so far include Del. Floyd Bagley (D-Prince William), one of the few who has actually announced; George Gilliam of Charlottesville, 7th District party chairman; and Sandra Duckworth, Fairfax County supervisor andDemocratic Party national committeewoman.