Washington's Metro subway is:

Attracting riders at record rates.

Winning favor from developers who want to build close to stations.

Facing its most uncertain year since 1976 because of a new national administration and mounting concern among local governments about transit's cost.

The inevitable result of those facts is that Metro's management will be forced to spend much effort keeping the subway construction program alive at a time when General Manager Richard S. Page is trying to improve the day-to-day management and operation of the nation's fourth-largest public transit system.

Metro's major gains in ridership have been posted despite record-setting fare increases. The fiscal 1980 ridership total for the combined bus and rail system was 187 million passengers after double-counting was eliminated, the highest transit ridership figure for the Washington area since 1954.

Metro's popularity with developers was never more evident than in October, when investors Allan Rozansky and Alan Kay won approval for a $100 million office building and hotel project to be constructed in conjunction with Metro's Bethesda station, which is scheduled to open late in 1983.

Metro has 37 miles of its planned 101-mile subway system in operation after opening the Blue Line extension to Additon Road in November. Opening dates can be reasonably predicted for 64 miles, but no new sections are scheduled in 1981 -- the first year since Metro started in 1976 that it has not expanded the rail system.

Sometime in the spring of 1982 the Red Line will be extended two miles north under Connecticut Avenue from Dupont Circle to Van Ness Center. Future extensions through Alexandria to Huntington in Fairfax County, to Shady Grove Road in Montgomery County and across the Potomac River at 14th Street will bring Metro to 64 miles by late 1983.

What happens after that will depend greatly on how much money the new Reagan administration and Congress are willing to spend. Pre-inauguration talk among Reagan's transportation advisers has been particularly antisubway, and aid for transit generally has been cited as one of the domestic programs that should be trimmed.

Jimmy Carter came to office four years ago with much the same view, but by the time he left, the Carter administration had become transit's biggest friend. Metro's success as a new operating subway within two blocks of the White House is credited by national transit leaders as having been instrumental in that change, despite the fact that a Farecard vending machine at McPherson Square refused to accept Rosalynn Carter's dollar bill one day.

One reason for the concern about the future of the building program is that the cost of heavy construction has increased about half again as fast as the consumer price index.Thus, Metro's once-grand plan to build 98 miles in 10 years for $2.5 billion has now grown to an official estimate of 101 miles in 20 years for $8.2 billion, assuming enough money is provided to get the job done by 1990.

If it takes longer than that and if Metro's annually adjusted inflation projections are too optimistic, that number will be too low. In fact, Metro is unofficialkly looking at an $8.8 billion estimate, and there are back-of-the-envelope estimates that exceed $10 billion is escalating dollars.

Capital expenditures, however, can be financed attractively through municipal bonds, and 80 percent of subway construction costs are picked up by the federal government. The real cost of Metro as far as local governments are concerned has little to do with that $10 billion figure.

Metro's annual operating budget for the combined bus and subway system is $276 million in the current fiscal year and is projected to reach at least $320 million in fiscal 1982. The costs of operating Metro fall first to the riders, who pay about half through steadily increasing fares, and then to local and state governments.

Federal operating aid, which Metro receives with other transit authorities under a national formula, equals about 20 percent of the total subsidy. Reagan's transportation advisers were particularly critical of operating assistance in a recent report, saying, "Operating subsidies for rail systems discourage local efforts at good management. Where possible, they should be eliminated."

Page, the first Metro general manager with experience at running an operating system, has been quietly cleaning house. New directors have been named in the past year in several key offices, and subtle but important organizational changes have been made or are in the works. The question is whether that effort will bear fruit soon enough to satisfy local governments, which have discovered that their Metro subsidy is second only to public education as a line item in the budget.

A particularly generous labor contract Metro inherited in 1973 along with four privately owned bus companies adds to management difficulties. That contract required that Metro pay its transit workers quarterly cost-of-living increases that matched the consumer price index in percentage. At the same time Congress approved money for the takeover, it also required that Metro settle all future labor issues through binding arbitration. The theory was to preclude a transit strike in the nation's captial.

Page believes firmly that binding arbitration is the antithesis of collective bargaining. Support for his position came in the recent contract settlement in which a neutral arbitrator continued most of the cost-of-living protection clause. Union leaders called it the best transit contract negotiated or arbitrated in the past year, a year which saw both Chicago and San Francisco authorities win major productivity increases after taking strikes.

Adding to those problems, and to the problems of accommodating a construction schedule to the political realities of a new administration, are the continuing disputes that divide Metro's eight local partners on a number of issues. They seem to be able to agree only when fighting the federal government.