An $18.8 million grant from the U.S. Department of Transportation to the Massachusetts Bay Transit Authority will permit construction of the John F. Kennedy Memorial Library to begin in June 1972.

The grant, which was part of a $33.6 million award to the MBTA announced yesterday in Washington by Senator Edward W. Brooke (R Mass.), will provide around two-thirds of the funds needed for the construction of an MBTA train-storage and repair station on the site of the now-vacant Penn Central railyards on Dover St. in Boston.

The MBTA now has the money to begin moving trains to Dover St. from the present Bennett-Eliot station on Boylston St. in Cambridge, the projected location for the Kennedy Library.

The chief stumbling block in constructing the library is now money, according to Richard E. Barringer, assistant dean of the Kennedy School of Government. He said last night that since the site will be clear in a little over a year. "We'll put up whatever there's money for, starting a year from next June."

Barringer said that the whole complex, which he said will include libraries for both Harvard University and the Institute of Polities in addition to the Memorial, will cost $18 to 20 million when finally completed.

Total funds available to the Kennedy School for construction alone are around $9 million, according to Barringer. There is another $10 million available to the School for the Memorial project but that money can be used only as a trust fund.

Barringer said that pre-construction testing of the site would begin this summer, "with firm intentions of beginning construction a year from next June." He said the main problem in actual construction would be seeing whether the wooden piles now in the railyard would provide sufficient support for the Library. If not, new piles would have to be driven.

Barringer said that at least one of the buildings will be up by 1976, "if enough money can be found."