Hundreds of thousands of proud and loud Redskins fans turned Pennsylvania Avenue NW into a massive line of scrimmage yesterday, greeting Washington's triumphant football team with tumultuous, if occasionally unruly, glee.

Government offices closed up tight, streamers and confetti fell through the air, souvenir vendors did record business and area teachers stood before half-empty classrooms as all Washington joined Mayor Marion Barry and President Reagan to celebrate the Super Bowl sensations.

But Assistant Police Chief Isaac P. Fulwood Jr., who estimated the crowd at 600,000, said police "lost the street" as the parade reached the District Building. The throng surged onto the street, snapping wooden barricades and pressing against the speakers' platform.

Police arrested 31 people, mostly for disorderly conduct and vending violations. At least 24 people required minor medical treatment; most felt faint from the press of the crowd. Other than one woman who broke a leg, there were no serious injuries, but it took much of the day to clear the area of fans, including rowdy teen-agers who had to be escorted from The Shops at National Place, the mall across from the District Building.

All of which did little to detract from the festivities. Everett Harris, a 28-year-old carpenter dressed in a Redskins hat and sweatshirt, blew on a silver whistle and delighted onlookers with his rendition of "Hail to the Redskins."

"I haven't calmed down since Sunday," he said. "In Washington we don't have a lot to celebrate, but this is something everyone can feel good about. Black and white, we are all one family when it comes to the Redskins."

"This is the greatest welcome anyone could pay to an individual, a team," said quarterback Doug Williams, the Super Bowl's most valuable player and the toast of the town. "This is a long ways from Zachary," his Louisiana home town.

Defensive star Dave Butz was more blunt. "We came, we saw, we kicked their butts," he told a cheering crowd at a pep rally at the District Building.

On a raw, cold and -- contrary to weather forecasts -- dry day, people began lining the avenue from early morning. By 11 a.m., the start of the parade, every available surface from Third Street to the District Building was teeming with fans bundled in burgundy and gold.

Although police said the crowd was larger than the 500,000 gathered for the 1983 Redskins Super Bowl celebration, other estimates of yesterday's outpouring were more conservative by half.

With a few exceptions -- notably a dozen or so teen-agers who traded punches and racial epithets outside the Pavilion at the Old Post Office -- the crowd was powerfully good-natured, cheering at speeches they could not hear, waving to players they could not see.

They wore every manner of Redskins paraphernalia. There were painted faces, Indian headdresses and even folks in gorilla and chicken suits.

Even the president took notice of the zaniness, saying at a White House reception for the team that some Redskins fans "wore hog noses. Some even climbed lamp posts. My staff told me that that wouldn't be very presidential. But make no mistake about it, I'm just as enthusiastic as your fans."

Amid all the good cheer, there was considerable fear, as human gridlock left many people immobilized on sidewalks. "Somebody's going to get hurt," Barry told fans at the rally. "Come on, back up. Back up. Take two steps back."

The entreaties resulted in more trampling and shoving than actual movement. "We've got to get more police here," Police Chief Maurice T. Turner Jr. said on the podium. A city government source said Turner had worried at a planning meeting Tuesday that a large crowd might overwhelm police.

As Williams began to thank the crowd, three people were passed hand over hand up to the rally stage; two were unconscious. None was hospitalized, according to the D.C. Office of Emergency Preparedness.

Fans packed rooftops, terraces, windows. They climbed aboard any available high surface, clinging precariously to the tops of benches, newspaper boxes, flowerpots, traffic lights, garbage cans, statues and even the spindliest of trees. The roof of a bus shelter collapsed under the weight of several fans; two people were treated at a hospital.

Ruben Garcia, an office painter, brought his stepladder outside, perched himself atop it and settled in for obstacle-free viewing. He saw a parade of D.C. motorcycle police, the Woodson, Cardozo and Fairfax high school bands, a procession of local politicians in convertibles and the Redskins tour buses.

Then the parade fell into disarray. Ebullient fans swarmed past police lines into the street. Ten mounted U.S. Park Police officers arrived within seconds and slowly coaxed the crowd back to the sidewalks. At 12th Street, people atop a moving van created a near-stampede by throwing to the crowd boxes of Wheaties cereal depicting the Redskins.

"I had to fight for it," said Jackie Briscoe, 22, of Capitol Heights, a smashed cereal box under her arm. "I fought just like everybody else did."

But while the Redskins proceeded without further disruptions, the rest of the parade never got back in gear. Fully 45 minutes later, well into the rally, the straggling Eastern High School band arrived, having just fought through the masses.

Many fans could have done without the long parade of politicians that preceded the players along the avenue. "These guys don't know how to run a pep rally," said Gwen Tiel, who came in from Fairfax to cheer the Redskins.

Although wild cheers and even hair-raising shrieks greeted the start of the parade, it wasn't long before the sounds changed to groans. The four two-car Tourmobiles carrying Redskins players was equipped with tinted windows through which the players seemed blurry shadows. "Really a disappointment," said Stephen Bark of Baltimore.

As in 1983, when the victorious Redskins rode along Constitution Avenue, the players were kept out of convertibles for security reasons.

But when Williams leaned out of the bus at Seventh Street to point his index finger high in the air, the responding roar could be heard for blocks.

The second loudest greeting went to Barry, who wore a burgundy cowboy hat and rode in a convertible surrounded by security guards. Barry was one of several elected officials who congratulated the team at the rally, which was marred by a weak sound system.

Sen. John W. Warner (R-Va.) declared the Redskins "America's team." D.C. Council Chairman David A. Clarke called Williams "the best role model in the area."

Rep. Steny Hoyer (D-Md.) also congratulated the team, and Audrey Moore, chairman of the Fairfax County Board of Supervisors, showed her support by riding in the motorcade.

Even as D.C. officials savored the Redskins' triumph, they received an ultimatum from team owner Jack Kent Cooke, who said he would renew his effort to build a stadium in the suburbs unless the city produces a "solid proposal" for a new stadium by June 30.

"Failing that, then it's going to be necessary for us to go to one of the surrounding counties and say, 'We've exhausted every means of keeping the stadium in D.C.,' " Cooke said in an interview aired last night by WJLA-TV.

Cooke, who is seeking to move his team from the 55,750-seat RFK Stadium to a 75,000-seat domed stadium, said he was awaiting bids from the suburban counties. But he added, "I still prefer to stay in the District of Columbia, and I cannot say it too often."

After the rally, at a District Building reception, Williams and Barry posed with a cake in the quarterback's likeness. Players and politicians dined on ham, goose liver pate, stuffed shrimp and mushrooms stuffed with crabmeat.

Defensive end Dexter Manley yelled his way past autograph seekers. "Hey, outta the way," he said. "I gotta make a call."

He picked up the phone on Barry's desk and said, "Hey, Mr. President. This is the mayor, Mayor Manley. If George Bush doesn't answer those questions, I'll come over and answer them. Put them in writing, please." In San Diego, Manley had insisted that reporters write down their questions.

Earlier, at a Capitol Hill reception sponsored by Del. Walter E. Fauntroy (D-D.C.), players became impatient. Fauntroy cut the speech-making short.

The scene was more serene at the White House, where a crowd estimated by the White House at 3,000 people gathered on the South Lawn to watch Reagan shake hands with Redskins players and accept gifts of a team jersey and a football.

Williams, calling a play, gave the ball to the president "on one condition. If you run the right play and the play is trips right, fake zoom, Larry criss-cross and he's got to throw it."

The Gipper rose to the challenge, shouted, "Where's Ricky Sanders?" and passed the ball to the receiver, leading him like a pro.

The day began with crowds arriving from all directions. Many downtown streets were closed, but traffic tie-ups were minimal. Metro added rail service and rerouted buses; the rail system reported 200,000 trips during midday, twice the usual number. The Federal Triangle station closed about noon to prevent overcrowding.

The crowds had more than travel in mind. Virtually every one of 3,200 public service posters depicting Williams urging the public not to vandalize Metro vanished yesterday, said Metro spokeswoman Beverly Silverberg.

The post-rally scene was even more hectic. Police urged celebrants to clear the streets. "Go home, please, go home," a smiling Officer C.L. Walker pleaded.

At The Shops at National Place, police went store to store to clear crowds after shopkeepers reported grab-and-run thefts. Tom Tague, security chief for the building that houses the mall, said about 20 D.C. officers restored order after 10 lower-level stores closed because of crowding and theft. At the Foot Locker shoe store, more than 100 people filled a shop that gets crowded with 40. Employees chased shoplifters out the door.

"The kids just came in here and started grabbing stuff," said Paige Conrad, manager of Brooks Fashions, which suffered thefts of several sweaters and sport jackets. "I had to lock the doors twice to keep control."

For blocks, bushes were crushed and stray gloves and scarves littered the ground. Pedestrians had to step over tree limbs snapped off by fans seeking better views.

Government workers who parked in the lot next to the District Building found their cars had been used as viewing posts and alternative footpaths. About a dozen cars were vandalized; the roof of a van caved in.

Stephen Baker came out of his office at the Commerce Department after noon and saw people climbing over his car. "They pushed in my sunroof," Baker said. "They ground through the paint and there are shoe marks all over it. There were police nearby but they didn't do anything. It's irresponsible. Now I have this car that turns heads for the wrong reason."

Many in the crowd were schoolchildren who took the day off -- with or without parental permission. "Pretty much everybody is here," said Tamisha Kelly, a 10th grader at Elizabeth Seton High School in Bladensburg. Kelly and friend Beverly Twitty had front-row positions to show off the players' uniform numbers drawn on their cheeks with lipstick.

D.C. school spokeswoman Cheryl Johnson said attendance yesterday was about 50 percent, with much lower figures in higher grades. At Ballou High School in Southeast, for example, about 400 of 1,936 students showed up. In Fairfax County, high schools reported a 25 percent absentee rate, up from the usual 6 percent, said spokeswoman Delores Bohen. Montgomery County reported absence rates of 30 to 50 percent.

Many government offices never quite managed to get going yesterday. Although all District and most federal agencies encouraged workers to attend the parade, employees were supposed to work before and after the rally.

But many employees were on the street early to claim good positions, and cafeterias and other gathering places remained packed through the day. "Most people here locked up and left by 10," said Mary Foster, who had a warm viewing post at the Federal Trade Commission.

At D.C. Superior Court, the rendering of justice came to a grinding halt as most judges dismissed employees at 11 a.m. An exception: Judge Frederick Weisberg had given his jury a triple option on Tuesday. It could take a long break for the parade, skip the morning session and come in late, or start deliberating at 9:30 as usual and work straight through.

The jurors, veterans of a monthlong civil trial, voted to skip the parade.

There were more sedate celebrations around town. At Galt & Brothers jewelry shop, a window display was filled with a stately bouquet of burgundy and gold mums and a photo of the football team in a thick silver frame, all nestled in a fold of burgundy velvet. A small hand-lettered card announced, "Hail to the Redskins, Hail Victory."

Staff writers Lynne Duke, Tom Sherwood, Linda Wheeler, Nell Henderson, Michael York and Claudia Levy contributed to this report.