Flood waters from the rain-swollen Potomac and James rivers, which left widespread destruction in their paths during the last four days, reached the Washington and Richmond areas yesterday, causing millions of dollars in property damage, but no deaths.

The Potomac, which swept with raging fury past the steep cliffs near Chain Bridge and then flooded low-lying areas as it spread into a fast-moving, but somewhat gentler torrent south of Georgetown, crested in Washington nearly five feet above flood stage at 6 p.m. yesterday.

The high waters caused massive traffic tie-ups here and closed many businesses along lower K Street.

In Richmond, the James, which spilled into an 80-block area near downtown and forced the closing of a 15-mile stretch of Rte. I-95, crested at nearly 22 feet above flood stage before 2 p.m. Flooding in both areas was the most severe since Hurricane Agnes in 1972.

The confirmed death toll from the floods during the last four days, according to officials, stands at 37, with 46 persons reported missing. Eighteen of those fatalities occurred in West Virginia, 17 died in Virginia, and Maryland and Pennsylvania each reported one flood-related death.

Damage in the four-state area is still being assessed, although more than $550 million worth of property destruction has been estimated for Virginia and West Virginia. Thousands remained homeless.

In Washington, flooding yesterday closed several low-lying highway arteries, including stretches of the George Washington Memorial Parkway, and brought morning rush-hour commuters to a standstill at many places.

Restrictions on I-66 and I-395 commuter lanes were lifted for the evening rush hour, shortening commuting delays, but authorities were uncertain late yesterday if waters would recede enough to permit the parkway to reopen for this morning's rush hour.

But for many, particularly those lured by the bright sun and blue skies, the flood scenes yesterday were more an occasion for curiosity than concern. For every person who nervously hauled in sandbags to protect a shop or residence, there were six times as many gawkers for whom the menacing river was a new tourist attraction.

"Being on the fringe of a natural disaster that won't touch you is rather exciting," said Malin Basil, a resident of the higher reaches of Georgetown, who took her 2 1/2-year-old daughter for a stroll along the waterfront.

A party atmosphere pervaded the Georgetown area, prompting a catering firm to set up a streetside spread of raspberry butter cookies, chocolate and almond cookies and coffee, served from a silver samovar.

The mood was much the same in Old Town Alexandria. At midafternoon, as water inched up King Street toward Lee Street, Mayor James P. Moran rowed past in a gondola complete with ornamental maiden at the prow.

Moran, District officials and representatives of the National Park Service worried about the cleanup to come, but stealing a glimpse of the high waters occupied others.

Inside the Watergate office building, Debbie Rizzo, a law firm secretary, said fellow workers had been dropping by her 10th-floor office all morning to look at the river.

"People stop in, check it out, get a flood report," she said cheerfully.

From his helicopter, WTOP radio traffic reporter Bob Marbourg's view was partially obscured by morning fog -- but what he saw was enough to know things were bad.

Comparing the monumental traffic tie-ups with those that occurred after an 18-inch snowfall two years ago, Marbourg said commuter traffic on Rte. 1 was four times heavier than usual and that cars were backed up to Beacon Mall in Fairfax County.

"It was such a beautiful day, but then you'd look down and see where mobile homes were on their sides and the houses were under water and the river was a mile wide in some places," said Marbourg, describing the scenes near Point of Rocks and Dickerson, Md.

Water submerged the southernmost parts of the C&O Canal and Towpath, which has taken a beating from flood waters all along its 184-mile route between the District and Cumberland, Md. Officials said that no damage estimate was available for the northern reaches of the canal, where high waters have started to recede, because all their attention was focused in the south, where Locks 1 through 5 may have received damage from raging water.

"Lock 5 above Chain Bridge is always a weak spot because the Potomac constricts and narrows there," said National Park Service spokesman Earl Kittleman, "and when there is a flood, the waters are rushing very, very fast. It's not only the speed but the volume and the pressure" that can cause damage.

As the water level goes down, Kittleman said, authorities may discover major damage to the canal, the entire length of which was closed Tuesday for the first time.

"What happens in high and fast-moving water is that it undermines the earth and it all washes out," Kittleman explained. "Once that happens and the flood water recedes, then you essentially have a hole in the canal and you can't put water back in until you fix the breach."

For the people who keep statistics on such things, there were plenty to be had. But the flood levels were not a record in either Washington or Richmond, according to the National Weather Service.

The rain-soaked and muddy James River failed to swell to its predicted crest of 27 feet above flood stage, and yesterday's Potomac River flooding was a far cry from the great 1889 flood, when the waters rose to 19.5 feet. The infamous Hurricane Agnes crested at 15.4 feet, according to measurements taken at the weather service's Wisconsin Avenue station.

From the U.S. Geological Service, officials said the water flow was only the fifth highest in record, about 207 billion gallons' worth when the river crested at Little Falls yesterday afternoon. Also yesterday, about a half million tons of sediment moved down the river.

"We're not counting logs and houses, just sediment," said spokesman Donovan Kelly.

As is usual in emergencies or feared emergencies, authorities took steps to minimize trouble. With the parkway closed, National Airport passengers were urged to use the Metro lest they become snarled in Rte. 1 traffic congestion.

Utility spokesmen said service was halted in several areas as a precautionary measure. Washington Gas shut off service to 24 buildings in Alexandria's Old Town and to four town houses in Georgetown. Virginia Power cut off electricity service to the 100 block of King Street at the request of the city of Alexandria.

Specially designed floodgates that surround the Washington Harbour project on the Georgetown waterfront performed "just wonderfully" in protecting the $200 million development from flood waters, said project manager Ron Eichner. No water entered the buildings, he said.

He said a comparatively small amount of water seeped into a pool on the river side of the development as a result of heightened pressure on groundwater, which in turn exerted pressure on a drainage system. When construction is complete, the strip between the gates and the pilings at the river's edge will be waterproofed, barring the imposition of such pressure and eliminating seepage, Eichner said.

But for all the preparations, yesterday's flooding in the region will be remembered by many for its picturesque scenes rather than its problems.

At the Tidal Basin, the sidewalk was impassable and areas along the basin were under water. The Jefferson Memorial looked like a giant birdhouse in the midst of countless low-flying seagulls, apparently drawn by the surplus of fish that the roiling waters had deposited in the basin.

And all along the Potomac, people, some with cameras, stood on banks and bridges to watch the river flow. The trees were at the peak of their fall foliage and surrounded by swirling, muddy water, so that the foliage started where the water stopped.

Despite 30 mph currents that were five times as fast as normal, police reported that numerous kayakers, canoeists and others had to be chased off the Potomac.

"There were all kinds of nuts out there today," one U.S. Park Police officer said.

Police said that no one had to be rescued yesterday from the swirling waters of the Potomac, although a few small boats that had broken from their moorings were retrieved and towed to shore.

But while the immediate Washington area found the floods more delightful than destructive, the same could not be said for other river neighbors.

In Virginia and West Virginia, the areas hardest hit by the floods, the slow and costly process of mopping up had to begin.

At the request of Gov. Arch Moore, President Reagan yesterday declared as federal disaster areas eight West Virginia counties where 4,000 homes were destroyed.

In Virginia, Gov. Charles S. Robb took a helicopter tour of the Richmond flood areas. An estimated 18,000 homes in the state were under water or damaged by the flood.

In Richmond, three of its seven bridges, including the I-95 span over the James, were closed. But the city's water plant, which authorities earlier feared might suffer flood damage, was spared.

Maryland's flood damage was the most serious in the state's western panhandle, although cleanup crews had already begun their work their yesterday. More than 1,000 persons statewide were left homeless.

In the District, military bases were among the areas most threatened by flood waters, and workers were sandbagging Fort McNair, Bolling Air Force Base and the Washington Navy Yard, where a spokesman said more than 100 tons of sandbags were piled up to protect buildings.

Weather officials, whose job it was to predict flood levels, said they were handicapped because Monday's storm knocked out their river gauges and most telephone communication lines, making it almost impossible to get adequate rainfall information. "We were just guessing," said National Weather Service hydrologist Leo Harrison.

In comparing this flood with Hurricane Agnes, for instance, Harrison said the flood levels were less this time in the Washington area because the distribution of rainfall was different.

Scientists watching the flood for its effects on water quality and wildlife in the Chesapeake Bay say the damage will have to be studied after the deluge.