While President Reagan and Soviet leader Mikhail Gorbachev search next week for new ways to control nuclear arms, some District motorists will simply be looking for new ways to get to work.

D.C. police announced yesterday that sections of four streets in Northwest Washington will be blocked four days for security reasons.

Police said the following areas will be closed from 12:01 a.m. Monday through Thursday night, when Gorbachev leaves town: 16th Street NW between L and M streets, which is the block in front of the Soviet Embassy.

Pennsylvania Avenue North between 13th and 14th streets. That is the block of the J.W. Marriott Hotel, where an international press briefing center will be located.

The curbside lanes of 15th and M streets immediately fronting the Madison Hotel, where some Soviet diplomats are staying.

Because of the prospect of traffic tie-ups, police also are urging motorists to avoid the area between 15th and 17th streets from Massachusetts Avenue to K Street. In addition, some anti-Soviet demonstrations are expected to congregate -- and disrupt traffic -- near 16th and K streets, the closest point ralliers can get to the Soviet Embassy under city law.

Driving may be difficult in that area early Saturday afternoon because of a prodisarmament rally. And driving on Constitution Avenue could be difficult Sunday afternoon because of a rally on the Mall on behalf of Soviet Jewry.

Officials said they will increase the number of officers directing traffic downtown during the summit.