Regents of the Smithsonian Institution voted yesterday to spend $70,000 to study the possibility of building as many as three underground garages beneath the Mall for parking up to 2,500 vehicles.

Michael Collins, new undersecretary of the Smithsonian, said an already serious traffic problem will become worse this ssummer when the new East Wing of the National Gallery of Art opens.

Building underground garages would require the approval of numerous agencies, including Congress. Collins said Smithsonian officials already have discussed the idea with the D.C. government, the National Park Service, the Fine Arts Commission, Council of Governments and Metro.

Among questions to be explored by the study, which will be financed with Smithsonian trust funds rather then tax money, will be where the garage entrances could be located, who would operate the garages and what effect they would have on public transportation.

The area to be studied for possible underground parking extends from 4th to 14th Streets NW along the Mall.

Metro spokesman Cody Pfanstiehl said, "We're not telling them whether to do it or not," but he said the construction would require "tearing up the Mall for a long time. It would be an awful mess."

He noted that the Mall entrance to the Metro was paid entirely with federal funds because it is used primarily by tourists. Although no date is set for start of Sunday subway service, Metro will begin operating on Saturdays this fall.

"The Fine Arts Commission worries about ugly air shafts" sticking up on the grassy open spaces of the mall, said John F. Jameson, assistant secretary for administration.

The Smithsonian now has 450 parking spaces beneath the Air and Space Museum and about 600 spaces above ground on the Mall drives.

Collin, who moved up to the number two spot at the Smithsonian behind Secretary S. Dillon Ripley on April 24, briefed reporters after the three-hour regents meeting that was, as always, closed to the public.

Collins indicated that Chief Justice Warren E. Burger, who serves as chancellor, and the other regents devoted little time yesterday to discussing recent criticisms of the Smithsonian. The most recent salvo was contained in a study for the House Appropriations Commitee that sharply criticized Ripley and his staff for "exercising a deliberate policy . . . to avoid accountability" for the more than $100 million in federal funds the institution gets each year.

The executive committee of the regents earlier this week hired a management consultant, however, to study how to improve relations between the Smithsonian and Congress, Collins revealed. The consultant, Hermann P. Bretsch, who will be paid $200 a day plus expensed for the 75-day contract, will study whether the Smithsonian needs to revise its bylaws and operational procedures.

Also, apparently in response to criticism that hundreds of Smithsonian employes have been switched between public and private payrolls "to frustrate merit system objectives," the regents ordered that a record be kept of the reason for each such future transfer, Collins said.

The board also approved publication of two new popular books, on inventions and field expeditions, after hearing that its first such effort, "The Smithsonian Experience," has produced a profit of $2.1 million this year.

The regents also urged the staff to acquire by transfer from the General Services Administration the Tariff Building on F Street between Seventh and Eighth streets to hold the overflow of exhibits from the National Collection of Fine Arts and National Portrait Galleery.