More than 200,000 persons -- double the original estimate -- and thousands of cars and buses are expected to jam the Mall and tie up traffic in downtown Washington Saturday during the national Solidarity Day rally, according to U.S. Park Service officials and D.C. police.

"Upwards of 200,000 is a good figure," said Donald Heilemann, a National Park Service spokesman, who said the estimate was based on information provided in planning meetings with AFL-CIO officials, chief organizers of the rally to protest the Reagan administration's domestic policies.

The AFL-CIO has publicly said only that more than 100,000 demonstrators are expected.

To help control the crowds, special traffic and parking restrictions downtown and in the Mall area will be in effect for the day-long demonstration.

Police are urging protest participants and the city's regular Saturday shoppers and tourists to take advantage of free rides on the Metro subway. The AFL-CIO leased the subway system for $65,000 to provide the free service for all riders from 8 a.m. until midnight.

The demonstration crowd is expected to begin converging on downtown Washington streets as early as 8 a.m. as marchers gather on the Washington Monument grounds and Ellipse just south of the White House to picnic and listen to entertainment.

At noon, the demonstrators are scheduled to step off down Constitution Avenue toward the Capitol for a rally and round of speeches planned for 3 p.m. to 5 p.m.

Union officials have been reluctant to discuss how many persons they expect, fearing that a less-than-advertised turnout may damage the credibility of the rally aimed at protesting Reagan adminstration social service budget cuts. Some organizers also indicated that leaders of the rally have purposely underestimated the crowd so that a larger turnout would appear more dramatic.

The protest, the first major public demonstration against Reagan, is supported by a broad-based group of more than 200 labor, civil rights and other organizations.

The National Weather Service has forecast a clear sky and mild temperatures for the day.

Park Service officials said union organizers have shown them computerized lists and other data that indicate as many as 5,000 buses are expected to roll into Washington from around the nation for the march and that most of the buses will carry from 40 to 50 people each.

Amtrak officials said they have scheduled 10 special trains, each with 1,000 persons, to arrive in Washington today and Saturday, in addition to regular service, reservations for which are greater than normal.

Rally organizers have said they expect about 35 percent of the crowd to come from the Washington metropolitan area.

Park Service officials also said they required organizers to provide one portable toilet for every 200 persons expected and that 760 toilets have been set up on the Mall, enough to serve the needs of about 150,000 people.

D.C. police officials said that Constitution Avenue, which runs parallel to the Mall's north side, will be closed at 7 a.m. Saturday from 15th to 23rd streets NW. The rest of Constitution Avenue from 15th Street to Pennsylvania Avenue at Third Street will be closed from 9:30 a.m. until the crowd disperses.

The 14th Street Bridge, which is undergoing renovation, will be one-way into the District until 9:30 a.m. and then closed until 4:30 p.m. when police will reopen it to outbound traffic only.

Officials said no parking will be allowed on Independence Avenue near the Mall and Smithsonian museums and will be closed off from First to 15th streets NW at 5 p.m. to help move the crowd from the Mall.

Police said north-south streets that cross or go under the Mall -- Third, Fourth, Ninth, 12th, 14th and 17th streets -- will be kept open as long as possible and closed only to allow the march to pass through intersections. Bus and car parking lots will be open at RFK Stadium, the Pentagon and the New Carrollton Metro station.