Thousands of people in the West were evacuated today as the heaviest rain in 31 years forced rivers over their banks and landslides blocked highways and railroads.

At least 10 persons were killed and four missing since the first in a series of storms struck a week ago. Since then, up to 19 inches of rain has fallen on parts of California and about 9 feet of snow in some western mountains.

Officials began assessing the millions of dollars of damage during a lull in the rain this morning.

But a new storm hit the San Francisco area in late afternoon, and the National Weather Service here said still more violent weather systems were heading inland from the Pacific.

"Right now, we don't see any sun for the next several days," said weather service forecaster Robert Brown.

Gov. George Deukmejian issued disaster declarations for Humboldt, Sonoma and Napa counties to clear the way for federal aid for flood victims. The governor said that he is expecting requests from other counties before the storms subside.

At a Santa Rosa evacuation center north of here, Don Miner said he paddled a canoe to safety from the inundated Russian River resort town.

"As we rode out," Miner said, "we were going right over people's houses. The power lines were literally inches from our heads. All we could do was push them aside with wet newspapers and hope for the best."

Miner's wife, Betty, said she saw a cabin float off its foundation and sink. "It was like that everywhere, destruction everywhere," she said.

The powerful storms began last Wednesday and gathered momentum Friday, with only brief respites. In northern California:

*An estimated 10,000 people were forced from their houses at various times because of flooding, according to statements by authorities in the half-dozen counties most affected.

*Marin, Solano, Santa Cruz and Santa Clara counties estimated that their combined property damage from the storm would total at least $30 million. But that estimate, which did not include figures for hard-hit Marin, Napa and Sonoma counties, was expected to increase as officials continue their inventory.

*Flooding left the towns of Sebastopol, Guerneville and Monte Rio isolated, while mud slides blocked major freeways and cut train service as the main line from the Midwest into northern California was blocked.

*Interstate 80, the route between San Francisco and Sacramento, was shut this morning because of a slide at Fairfield, the first such closure in a decade. Motorists were forced to detour through Stockton.

*An earthen dam on the Sacramento River above Auburn collapsed under the pressure of water flows in excess of anything officials had seen since the last big flood in 1964.

Twenty-four-hour rainfall in parts of the Coast Range in Napa and Sonoma counties exceeded 8 inches, with 11.15 inches at Atlas-Dutra in Napa, the weather service said. Kentfield in Marin County had about 19 inches of rain since Feb. 12, the agency said, and the Heavenly Valley ski resort reported 9 feet of snow. In Utah, Wellsville had 10.56 inches of rain in five days, and Bald Mountain, Idaho, got nearly 50 inches of snow.

"You'd have to go back to 1955 to find the kind of values that we are seeing in the last 24 to 48 hours," forecaster Jim Henderson said in Redwood City, Calif.

An avalanche Monday cut off about 500 people at June Lake, Calif., a ski resort near Yosemite National Park. Colorado's Avalanche Information Center said literally hundreds of avalanches were occurring in western states.

Said weather service meteorologist Bill Alder in Salt Lake City: "The melting of the snow and the added rainfall are making things rather unstable."