Special parking restrictions will be in effect and some streets around the Mall will be closed temporarily during today's national Solidarity Day demonstration, an event that officials estimate may draw as many as 200,000 people to protest President Reagan's domestic policies.

Police suggested that participants, tourists and shoppers use the Metro subway, which will be free for all riders from 8 a.m. until midnight. The AFL-CIO, organizer of the march, paid $65,000 to provide the subway service.

Marchers are to begin gathering on the grounds of the Washington Monument and Ellipse about 8 a.m. for picnicking and entertainment. About noon, a march will step off down Constitution Avenue, leading into a rally from 3 to 5 p.m. at Third Street NW and the Mall.

No parking will be allowed on either Constitution or Independence avenues.

Constitution Avenue from First Street NW to 23d Street NW will be closed to vehicular traffic from 7 a.m. until the crowd disperses.

Independence Avenue from First Street to 15th Street NW will be closed at 5 p.m. to allow the crowd to disperse.

The 14th Street Bridge will be one-way inbound until 9:30 a.m., then will close and reopen at 4:30 p.m. for outbound traffic only.

Police said north-south streets crossing through or under the Mall will be kept open except to allow the march to pass.