The multibillion-dollar question of how to make the nation's public transportation systems accessible to the physically handicapped was delivered to the Metro board yesterday in an inch-thick document.

"I agonize over proper recommendations to you on this issue as much as (if not more than) any other issue . . ." Metro General Manager Theodore C. Lutz wrote in a cover memorandum to the board.

Washington is lucky, because its new subway system already has an elevator at every station and trains with doors wide enough to accept wheelchairs. The only thing Metro has to decide is whether to make all of its 1,800 buses fully accessible by replacing them over several years with buses costing $10,000 to $30,000 more - a mere $18 million to $54 million, 80 percent of it federal.

But the cities with old subway systems - notably New York, Philadelphia and Boston - face costs totaling billions of dollars if they have to put elevators into all their old subway stations.

"We didn't put a price tag on intergrating other minority groups into this society," Rick Dudley said yesterday. He is with the Paralyzed Veterans of America and his statement draws the line where they physically disadvantaged group sees it: as a civil rights issue.

The federal Urban Mass Transportation Administration, in proposing regulations recently that would require elevators in all old subway stations, estimated it would cost $1.6 billion in 1977 dollars to do so.

"We believe that figure is grossly underrestimated," said Stanley Feinsod, vice president of the American Public Transit Association, which represents most public transit systems nationwide.

"It will cost between $1.5 billion and $2 billion just to do New York City's 472 stations. Furthermore, the Department of Transportation has not even done an economic assessment on what Transbus will cost."

Transbus is the bus everyone must buy after 1979 if they want federal aid in buying buses. Transbus has a low floor and a ramp for wheelchairs and is fully accessible to the handicapped.

Metro's Dave Gaul estimates that each Transbus will cost about $125,000. The newest buses being built cost about $92,000 to $97,000. The last buses Metro bought - the old kind - cost $82,000, including a wheelchair lift of unproven reliability. Metro will start using them here in a few weeks.

Lutz recommended to the Metro board yesterday that Metro experiment with the 130 lift-equipped buses and be prepared to add lifts to an additional 130, which can be easily fitted.

Furthermore, he suggested that the board might wish to institute some kind of transit-on-demand, where a wheelchair-bound person could telephone and receive dor-to-door bus service.

Neither Lutz nor anybody else knows, however, whether a transit-on-demand program will be acceptable when federal regulations are completed and, doubtless, tested in the courts.

Several cities, including Baltimore, have attempted to meet the handicapped need with transit-on-demand service. "Basically our position is that it is inappropriate when we are offered a segregated service," said Dudley of the Paralyzed Veterans of America.

The American Coalition of Citizens with Disabilities, of the which Paralyzed Veterans is a member, has been staging demonstrations around the country in favor of Transbus, which has become the symbol of the accessibility issue in transit.

The coalition is seeking to build pressure against a provision of a bill in a House committee that would require further study of the Transbus questions. In the view of Transportation Secretary Brock Adams, it has already been studied to death.

"Transbus should be built and we should have it on the streets," Adams said in a recent interview. "It is a benefit for the elderly. It is also projected to be a benefit for the handicapped in that you roll wheelchairs on to it."

Adams also said the status of the law and the accessibility regulations is such that he has no choice but to require the ultimate refitting of existing subway stations. "It's done," he said. "As far as we're concerned it's within the evaluation and review group."

The Council on Wage and Price Stability is reviewing the regulations requiring full accessibility because of their possible inflationary impact.

General Motors and Grumman Flixible, two bus manufacturers, are displaying in Washington this week their answers to the bus supply problem - and their answers are one step short of Transbus. Both models "kneel," or lower themselves at the curb, to make boarding easier. Both can be fitted with wheelchair lifts.

The GM bus lift is in the back, which bothers Lutz. "There's the symbolic problem with the back of the bus," he said. "Furthermore, the driver has to get out and go to the back to collect the fare."

Metro is planning to purchase about 100 buses this year as part of its continuing program to keep the fleet current. Final Metro board action on Lutz' recommendations yesterday is scheduled within four weeks.