A proposal to study the feasibility of extending the Metro rail system far beyond its original 100 miles was approved by a Senate subcommittee yesterday.

The study, proposed by Sen. Charles McC. Mathias (R-Md.), is similar to legislation introduced in June by four area members of the House. Both proposals could add 47 miles or more of rail service linking Dulles Airport, the Capital Centre and such booming outlying developments as Bowie and Germantown in Maryland and Reston and Burke in Virginia. Additional lines also would be added in the District.

The House bill calls for $1.5 million in federal funds and $300,000 in local money to finance the study. The Senate version does not authorize an appropriation, but would leave the U.S. transportation secretary and the board of directors of the Washington Area Metropolitan Transit Authority.

Even though less than half of the original system has been completed, and the full 100 miles will not be operational for another 10 years, Mathias said a study of possible expansions would provide " a starting point from which we can begin looking at the long-term future and adaptability of the Metro rail system."

Rep. Herbert E. Harris II (D-Va.), chief sponsor of the legislation in the House, said Mathias' action provides "strong impetus" toward the possible expansion of the popular mass transit system.

The Metropolitan Affairs subcommittee of the House District Committee has scheduled a hearing Sept. 17 on the extension study. But Mathias employed a legislative technique yesterday that bypasses the hearing process in the Senate.

Mathias offered his idea as an amendment to the 1981 Transportation Department budget. It was accepted during a markup of the budget yesterday by a transportation subcommittee of the Senate Appropriations Committee. If the amendment stays in the budget when it goes before the full committee and on the Senate floor, it would be one of the differences to be ironed out in a conference with the House, which has no such provision in its version of the 1981 budget.

Mathias, a member of the transportation subcommittee, said "as the Washington metropolitan region grows, the demand for expansion of the existing Metro system is certain to grow. The studies will provide an orderly way of projecting and managing that expected growth."

The Mathias and Harris plans are virtually identical in the areas proposed for study of expanded rail service. Both plans make sure that the three areas whose taxpayers provide funding for the system -- the District, Northern Virginia and suburban Maryland -- each get a slice of the additional package.

Areas that would be studied for extensions are:

Maryland -- 43 miles of the Blue Line, from the Addison Road terminal in Prince George's County, past the Capital Centre in Largo, northeast to Bowie; and six miles along the Red Line, from its planned terminus at Shady Grove Road in Montgomery County north through Gaithersburg to Germantown.

Virginia -- 10 miles on the Yellow Line from I-95 and the Springfield station to the vicinity of State Rt. 645 near Burke in southern Fairfax County; and an 18-mile addition to the Orange Line, either along the Dulles Access Road or I-66, connecting Tysons Corner, Reston and Dulles Airport.

District -- On routes to be determined by WMATA, in consultation with the mayor and city council, perhaps along H Street NE and NW.