Montgomery County will install 100 bicycle lockers and bike racks at the new Metro subway station in Silver Spring when it opens this fall and at four Metrobus stops in county shopping centers.

If successful, both lockers and bike racks will be installed at other Montgomery County and Prince George's County Metro stops as they open over the next half dozen years to encourge bicycle-Metro commuting.

More than 18,000 residents in the two counties now pedal to work in good weather, and more than 22,000 will be commuting on bicycles by 1985, according to a regional bicycle use study now being completed for Metro and the Metropolitan Washington Council of Governments. Safe storage places for bicycles is considered crucial by bike commuters and would-be commuters if bicycle use is to grow in the Washington area, the survey found.

Within the next eight years the study estimates 4,700 of the projected 22,000 bike commuters in the two counties will be cycling to Metro subway stops. More than 250 bicycle commuters a day will make trips to and from nine of the 24 suburban Maryland subway stations. The Chillum-West Hyattsville station is projected to be the most popular, with estimates of 470 bicyclists a day by 1985, primarily because the station will be accessible to bikeways.

Fifty bike racks and 50 steel lockers will be installed at the Silver Spring Metro subway station, the first suburan Maryland Metro station to go into operation. An additional half dozen racks and lockers will be put near Metrobus stops in Wheaton Plaza and in Wheaton near Connecticut Avenue and Viers Mill Road, and at Glenmont and White Oak Shopping Centers.

In the District, 20 bike lockers will be installed this summer at each of five Metro subway station (Du-Pont Circle, Foggy Bottom, Union Station, Rhode Island Avenue and Potomac Avenue SE). Bike racks also will be installed at many stations and in July when Metro moves into Northern Virginia there will be bike racks - but not lockers - at all Arlington stations except for National Airport. And Metro is now attempting to get bike lockers there.

The lockers, which completely enclose the bicycle, have been used for several years in San Francisco's BART subway system. They probably will be rented here on a monthly basis, at the same $5 a month rate that BART charges, says Eileen Kadesh, bicycle coordinator for the D.C. transportation department.

The steel lockers cost between $150 and $175 and the bike racks cost about $25 for each bike slot. The District also is expected to install coin-operated bike racks to about 100 downtown parking meters. They cost about $60 each and also have been popular in California. It is not clear yet whether Metro of commuters will supply the locks for the lockers.

The study estimates about 590,000 bike trips a day were made here last fall, on an average sunny weekday, and predicts about 890,000 daily bike trips will be made in the Washington area by 1985 - most by children. There are 30,000 fair-weather bicycle commuters here now, the study estimates, and there will be about 53,000 by 1985.