Amtrak's trains are winning a steadily increasing share of the passengers who travel by air or rail between Washington and New York, a Federal Aviation Administration study shows.

During the past seven years, Amtrak's portions of the 3 million passenger market has increased from 27 per cent to 41 per cent. Seven years ago, airplanes carried almost three out of every four air-rail passengers between the two cities. Now, they carry only three out of five.

"We're well aware of the fact that we're in competition with that train," said Gilbert Barger, manager of departure services for Eastern Airlines at National Airport.

"We've always said that with good trains and good scheduled we could attract passengers," said Brian Duff, a spokesman for Amtrak.

However, the Metroliner and regular Amtrak service to New York lost $33 million last year that was made up by federal subsidies. Furthermore, a federal program totaling $1.75 billion is under way to improve the track between Washington and Boston and make it possible for a 120 m.p.h. train to go from Union Station to New york City in 2 hours and 40 minutes.

The federal emphasis on rail travel in the Northeast corridor is coinciding with concern about the energy crisis. Studies made are unanimous in concluding that railroads are a more energy-efficient way of carrying passengers than airplanes.

For example, a Department of Transportation study in 1974 found that a full train could average 270 to 360 miles per gallon of fuel per passenger, while a full airplane could get between 30 and 60 seat miles per gallon. For either mode to be truly efficient, however, all seats have to be filled.

One way to do that, transportation theory goes, is to keep the fares down. That is where Amtrak has the most obvious advantage over the airlines between Washington and New York.

Even after an increase scheduled June 1, the cost of a one-way coach seat on a non-Metroliner train to New York will be only $20; the Metroliner, an hour faster but not necessarily more comfortable, will cost $5 more.

A one-way plane ticket from National Airport to LaGuardia - Eastern shuttle or otherwise - is $38. There are excursion fares available uner certain conditions for both train and plane.

"Fares are part of the reason" trains are getting a larger share of the market, said FAA analyst Gene Mercer, "but other things have happened in the market as well."

American Arilines, which used to schedule hourly flights between National and New York's LaGuardia, has cut back to eight nonstops a day. American made that decision, despite carrying high loads, because it wanted to commit more of its quota-controlled take-off and landing slots at National Airport for flights to Chicago and Boston.

"We figured we weren't hurting the public, since Eastern has that shuttle every hour anyway," said an American spokesman.

But not everyone transferred from American to the shuttle, an Eastern official admitted. "We don't know exactly where they went," he said. The shuttle runs every hour on the hour; a seat is guaranteed and as many extra sections as are necessary are put on to underwrite that guarantee. Extra sections do not count against Eastern's airport quota.

As part of it response to the energy crisis, Eastern cut out its shuttles between National and Newark, and that loss is also reflected in the statistics concerning air and rail passengers. Whatever the reasons, however, 2.1 million people flew between Washington and New York in the fiscal year 1970 and 791,000 took the train.

But in fiscal 1976, 1.7 million flew, and 1.1 million took the train. The total air-rail market has remained about the same - somewhere close to 3 million people - during those years.

Amtrak has been steadily improving its equipment over the same period of time. Metroliners run virtually every hour, and conventional trains are available almost as often. Some riders find the regular trains more pleasant - there is more room to roam and a more appetizing food selection.

If travelers thave business downtown in either New York or Washington, the train provides door-to-door delivery. The plane offers the promise of an expensive cab ride at each end, which can do much to dissipate the two-hour advantage in actual trip time the plane has over the Metroliner and increase the overall travel cost.

As Washington's subway system expands and makes more of the city and inner suburbs readily accessible, Amtrak figures to benefit.

Despite the downward trend in air passengers in recent years, the Eastern shuttle is running four or five sections during peak hours, and traffic so far this year is up 14 per cent over last year, said John Stiffler, Washington manager of sales and service for Eastern.

A change in current operating rules and a great expansion in terminal facilities at National would be require before Eastern could put jumbo jets on the shuttle route, but such a change would provide more capacity per flight and is a possibility in the future, according to several sources.

The long-range trend for the Northeast corridor calls for increasing reliance on rail, according to planners. The airways are almost full, the highways are clogged, but here is still rail capacity.

"Given that," said Transportation Department policy planning analyst Arnold Levine, "the decision was that we would try and give a kick in the direction of more rail."