Congress and the administration soon must decide whether to extend or eliminate the experimental program that allows about one of every 10 civil servants to set his own hours or work a four-day week.

The program, which was initiated during the Carter administration and since has changed work patterns and car-pooling habits, is due to end this summer.

When flexitime was introduced in the late 1970s it was hailed as the way to expand service hours, virtually eliminate tardiness and boost morale and service time to the public. Congress authorized agencies to try out the program in the cities of their choice. Washington is one where it is being tested.

At its peak in 1981, nearly 600,000 civil servants, including about a third of the 350,000 feds here, were on some kind of alternate work schedule. It allows employes to come in as early as 6 a.m. or as late as noon, to work split shifts during the day or get long weekends by putting in four 10-hour days a week.

In recent years some agencies have curtailed or dropped flexitime schedules on the grounds that service to the public declined because managers failed to schedule work shifts or police the programs.

The Office of Personnel Management will complete its report on the state of flexitime, spelling out the administration's conditions for keeping the program alive, next week. Washington area congressmen, led by Virginia Republicans Frank Wolf and Stan Parris and Maryland Democrats Michael Barnes and Steny Hoyer, have rounded up 27 cosponsors for a bill (H.R. 1525) to extend the experiment.

Rep. Gary Ackerman (D-N.Y.), an advocate of flexitime, plans to conduct hearings next week before his human resources subcommittee of the House Post Office-Civil Service Committee.

The Reagan administration will probably seek to extend management controls on the alternate work schedules so agency heads can determine when to begin, expand, cut back or eliminate flexitime. Federal unions, and most members of Congress who favor the program, want it to be part of regular labor-management negotiations and guaranteed by contract.

If the program is chopped or ended, it would affect the commuting habits of thousands of feds from Reston to Fort Meade.