Despite delays caused by a shortage of rail cars and an impending fiscal gap estimated at nearly $3 billion, the Metro subway system is on the verge of extending new branches through Northern Virginia, Northwest Washington and suburban Maryland.

By the end of the year, rail service is scheduled to begin from National Airport through Alexandria to a stop near Huntington Avenue in Fairfax County. Stations have been built, tracks laid and tested, and sorely needed subway cars have started to arrive.

Next year, the Red Line is expected to open between the Van Ness-UDC station on Connecticut Avenue NW and the line's terminus at Shady Grove in Montgomery County. "This line, construction-wise, is right on schedule. And that is a little bit unique in this industry," Walter A. Mergelsberg, a Metro construction engineer, said as he pointed to a section of the Red Line in Montgomery County. Trains sped by, testing freshly laid tracks.

In 1986, rail service is scheduled to reach through Arlington and Fairfax counties to Vienna, running along the I-66 median where stations are now being erected.

Despite such auspicious signs, the transit authority's plans for expanding its rail network, built at a cost already approaching $5 billion, repeatedly have gone awry, most recently because of delays in deliveries of rail cars from an Italian manufacturing firm.

If enough rail cars were on hand, Metro officials have said, service to the Huntington station could have started last December and the line to Shady Grove could open by next December or January. Instead, both extensions have been set back about a year, with the Shady Grove station tentatively set to open late next year.

The delays in rail car deliveries have been attributed to interruptions in production at two plants that manufacture essential components--a Pittsburgh brake factory that was closed for nearly seven months by a labor union strike and a West German plant where a large press used to make exterior panels broke down.

Other sections of Metro's proposed 101-mile subway system, including the much-delayed Green Line, remain threatened by court challenges, controversies and fund shortages.

The Green Line, Metro's most hotly contested route, is designed to traverse inner-city Northwest neighborhoods, Anacostia and parts of Prince George's County. Construction on the line's southeastern branch has been blocked for more than a year by a federal judge's order in a dispute centering in Prince George's.

The rail system's financial uncertainties stem largely from two federal actions. First, the Reagan administration has agreed to finance only what it has described as "about 75 miles" of the planned system. The administration has left unclear both whether and when it might assume the costs of building additional mileage.

Metro officials, who have reviewed the issue with Urban Mass Transportation Administration aides, have interpreted the administration's position as providing for a 76.4-mile system, including the extensions to Huntington, Shady Grove and Vienna.

Funds would be available, officials have said, for two other Red Line stations--at Forest Glen, where construction is under way, and at Wheaton--as well as for a truncated portion of the proposed Green Line, including the section to Anacostia that has been barred by the courts.

This scheme, however, would provide no money for two outer sections of the Green Line, one extending through Northwest and Northeast Washington to College Park and Greenbelt and the other through Southeast to southern Prince George's. Also omitted would be a Northern Virginia extension to a Franconia-Springfield station and a Red Line station at Glenmont.

The second reason for uncertainty is that Congress' long-range authorization of construction funds is now considered insufficient to complete the 101-mile system.

Metro's total allotment would amount to $7.2 billion, according to Metro officials, if all federal and local sources were tapped. While this is about $700 million more than needed for a 76-mile system, it would fall $2.8 billion short of the probable cost of expanding the system to 101 miles, a sum tentatively estimated by the transit authority at $10 billion.

Moreover, key members of Congress already have raised new uncertainties. The House Appropriations Committee has recommended that financially pressed Washington-area governments be required in the future to pay a larger share of the Metro system's construction costs.

State and local governments now furnish 20 percent of Metro's construction funds, with federal appropriations supplying 80 percent. In metropolitan areas elsewhere in the country, congressional aides have noted, local governments have agreed to pay markedly higher shares.

Last week, a Senate move to restrain spending for subway construction set off protests from Metro officials. The Senate voted to allot $230 million to Metro for the next fiscal year--the same amount as the Reagan administration had proposed, but $45 million less than was approved by the House.

Metro officials charged that the proposed curtailment in spending would lead to delays of six months to 1 1/2 years in opening the Vienna and Wheaton extensions and in building several Green Line stations. An UMTA official disputed this view, arguing that additional federal funds are available from other sources.

Metro's plan for the Franconia-Springfield station has raised one further financial issue. Transportation officials have said this station would be sufficiently accessible to commuters only if a long-debated $200 million highway known as the Springfield Bypass is built nearby. According to Virginia officials, no money is expected to be set aside for the bypass for at least six years. Without the bypass, Metro and Fairfax County officials have said, opening the Franconia-Springfield station would likely prove to be a mistake.

With 42 miles of rail tracks now in operation, the transit authority is refining its plans for starting service on the 4-mile spur to Huntington and the 14-mile stretch to Shady Grove. Officials are examining how frequently trains should run, how much money the new service will cost and how soon the lines may open.

On the Huntington branch, a key issue is whether service should be provided by Blue-Orange or by Yellow Line trains. Huntington had been planned as a Blue Line station, but Metro officials recently proposed instead to incorporate it temporarily into the Yellow Line in an attempt to avoid further delays stemming from the continuing shortage of rail cars.

The Shady Grove branch is being studied by Metro, District and Montgomery County officials. They are seeking to determine whether the transit authority should open part of the line in mid-1984 instead of waiting until it has enough rail cars to provide service on the entire extension later that year.

The Grosvenor station near Rockville Pike south of Tuckerman Lane has been suggested as a temporary terminus. Montgomery County officials are also considering, as an alternative, the White Flint stop north of Nicholson Lane. Several Northwest Washington neighborhood groups recently urged the transit authority to open the Friendship Heights station at Wisconsin and Western avenues as an interim terminus early next year.

The sharpest controversies have focused on the Green Line. Its southeastern branch remains unbuilt largely as a result of an injunction issued in Baltimore by U.S. District Court Judge Norman P. Ramsey. His ruling in March 1982 stemmed from a challenge brought by business operators and residents in Prince George's who objected to a shift in the line's proposed terminus near Branch Avenue to another site near Rosecroft Raceway.

In Northwest and Northeast, the line's prospective route as it travels near Rock Creek Cemetery and Fort Totten Park has never been firmly decided because some plans sparked neighborhood opposition and other proposals have been viewed by Metro officials as too costly. Another dispute has arisen in College Park, where the City Council recently called for a shift in the site of a planned station.

Nevertheless, one Green Line stop--the Waterfront station at 4th and M streets SW--has long been built. With further construction halted by the court order, the station stands unused, its entrance barred with plywood boards. "It's just sitting there," said Albert J. Roohr, a veteran Metro planner. "We could grow mushrooms in it."

Along Metro's other prospective routes, construction crews are at work, sometimes within view of rush-hour commuters and sometimes hidden underground. About 200 feet below ground, workers are completing concrete foundations for platforms and tunnels at the Forest Glen station, situated west of Georgia Avenue in Montgomery County.

Some of the new lines are already marked by novel architectural embellishments. These include a domed underground rotunda at the Friendship Heights station, a square skylit station house at White Flint and ornate brickwork on station walls at the King Street stop in Alexandria.

And at least one station--the West Falls Church stop on the Vienna line--was laid out with an eye to the future. It was designed, according to Metro officials, to make it possible for a rail extension to be built someday to Dulles International Airport.

Although some officials have expressed hopes of offering rail service to Dulles, the transit authority has never drawn up plans for such a route, nor have funds been set aside.