Reveling in a driving rain that they blithely dismissed as "hog weather," more than half-a-million soggy celebrants crushed together yesterday along Constitution Avenue to welcome home the Super Bowl champion Washington Redskins.

The parade's start was delayed by surging crowds that blocked the route, frantically trying to glimpse the two Metro buses carrying the town's triumphant football team. Fans jumped up and down, climbed trees and shinnied up traffic-light poles, while police acknowledged they could not control the tumultuous celebration.

Lining the 12 blocks from the District Building to Third Street NW were fans with rain-smeared Indian war paint dripping down their chins, fogged-up glasses and limp World Champion pennants, squishy sneakers and hoarse voices. They squealed like hogs and whooped like Indians. They jumped up together in the middle of Constitution Avenue and slapped hands. They stole kisses from the Redskinettes. And, despite the cold rain, they said it was worth it.

"I've been going to Redskins games ever since I was old enough for my father to carry me. I'm here because I'm crazy," said Perry Collins, who sells office furniture.

When fans finally caught sight of the Redskins in the two buses--after anxiously peering into passing cars only to find waving politicians inside--many were seized with near hysteria. They broke through police lines, pounded on the buses, grabbed players' hands, threw bottles of champagne and beer through open windows and attempted to follow the procession down the avenue.

"It was something I'd never experienced before," said wide receiver Art Monk. "It sort of makes you feel that you accomplished something and that the whole community is behind you. It puts a chill through your body."

The crowd, which D.C. police said was as large as the throng of more than 500,000 that greeted the return of the American hostages from Iran two years ago, was too big and boisterous to be contained, said Assistant Police Chief Marty Tapscott. However, police reported no arrests related to the parade and no serious injuries.

"These people came down and stood in the rain to wait and see their Redskins, and we would have had to have a policeman for each spectator in order to keep them away from their heroes," Tapscott said.

The crowd was so thick on the street that the marching band from Walt Whitman High School in Bethesda had to give up the notion of marching at all, as did several other area high school bands.

Scores of area residents, many of whom had brought young children to the parade with them, complained angrily yesterday to police about the lack of crowd control.

"I am absolutely appalled at the District of Columbia for not having ropes up and keeping them back when the buses came by. When the buses came, the kids in the crowd started to surge and they just about trampled my child to death," said Marian Newman of Bethesda, who brought her 8-year-old daughter, Sarah, to the parade. "I've been in many protest marches and never felt this panicky before."

Before the parade, under a dripping canopy in front of the District Building, Redskin Coach Joe Gibbs hoisted the gleaming Super Bowl trophy over his head and ignited the cheers of thousands of fans massed under a sea of umbrellas and soggy "We Love Them Hogs" banners.

"No other fans in the world would come out on a day like this except in Washington, D.C.," Gibbs said. "Each one of you has a small piece of this trophy today."

Federal and District government employes were given two hours' leave, from noon to 2 p.m., and many streamed out of their office buildings to watch the procession. Students, however, seemed to constitute the largest and most rowdy part of the crowd, as area schools, which allowed students to attend the parade if they brought notes from their parents, reported high absenteeism. In Prince George's County, for example, 70 percent of junior and senior high students were reported absent.

"I'm proud to say about 75 percent of our kids are not here today," said Bobby Mullis, a Redskins fan and principal of Northwood High School in Silver Spring.

The crowd yelled long and loud for John Riggins, the running back and Super Bowl hero who was proclaimed by one banner to be "King John the First."

"We're just down here for a good time and to see our man John Riggins," said Pat Prada, a 16-year-old DeMatha High School junior.

Their man Riggins, however, did not make it downtown in time for the parade because he apparently overslept after arriving in Washington last night from California.

"I'm still home out here in Virginia. My plane got in last night and I didn't reset my watch," Riggins told an editor at WDVM-TV, in a phone call at 1:30 p.m. yesterday, about a half-hour after the parade had begun. The editor, Joe Palca, said Riggins had called, asking to speak to his friend Sonny Jurgensen, the quarterback-turned-sports commentator.

The television station dispatched a limousine that picked up Riggins at his home near Fairfax Circle and brought him downtown after the parade was over. Riggins did manage to show up at 3:30 p.m. at the Hyatt Regency Hotel for the tail-end of a private reception thrown for the Redskins and members of Congress, but many Redskins players had already boarded buses and members of the press had started to leave when the running back showed up. His appearance provoked a repeat of the pushing and shoving that had occurred earlier on Constitution Avenue.

"I thought the 'Killer Bees' were tough," Riggins said at the Hyatt, comparing the crush of reporters and spectators in the hotel to the Miami Dolphin defense.

Yesterday's parade, for which President Reagan had given government employes the two hours off, interrupted work throughout the downtown area for several hours. Those downtown on non-Redskins business complained about not being able to find a cab or anyone in government office buildings.

Rep. Stan Parris (R-Va.), put off a meeting with the Army Corps of Engineers yesterday to attend the parade only to learn later they wanted to discuss the possibility of moving Fort Belvoir, a military installation in his district. The meeting was hastily rescheduled for later in the afternoon.

The crowd began gathering downtown about 10 a.m. Metro subway stations in Maryland and Virginia were crowded with singing, cheering fans. Metro added more cars to handle the extra riders and trains reportedly ran on schedule.

The rain, which seemed to fall especially hard just when the Redskins drove down Constitution Avenue, failed to dampen the enthusiasm even of fans who had showed up with no rain gear.

"We'll all be sick tomorrow, but, hey, it's for the 'Skins," said Larry Hall, who took time off from his job laying concrete in Southeast Washington to attend the parade. His blue work pants were soaked and rivulets of water dripped onto his face from his white hard hat.

Bobby Thompson of Waldorf, who lays carpeting in the U.S. Capitol, was also drenched. His presence, his friends explained, was punishment for supporting the Dallas Cowboys.

"But this is worth two hours off from work," Thompson said, jovially wiping wet hair off his forehead.

Near the end of the parade, one cabbie, who said he couldn't move in all the traffic and who had finally given up taking passengers, had these final thoughts on the Redskins Super Bowl season:

"As far as I'm concerned, I'll be just as happy if it's another 10 years before we're champions again."