Two of the three members of the Federal Home Loan Bank Board plan to resign this summer, forcing the White House to pick replacements quickly or leave the board powerless during the most turbulent period of its history.

The two members are Donald Hovde and Mary A. Grigsby. The bank board, which regulates the nation's thrift industry, cannot vote on regulations or take other action without the participation of at least two board members.

Bank Board Chairman Edwin J. Gray said he has no plans to resign before his term expires July 1, 1987, and does not know who might replace Hovde and Grigsby but doubts that the White House would allow two vacancies to exist at the same time.

Hovde said yesterday that he has told the White House he intends to leave government and return to the private sector Aug. 31.

Hovde also noted that Grigsby notified President Reagan last month she intends to leave the board when her term expires at the end of June. Grigsby, the board's lone Democrat, was traveling and could not be reached for comment.

Hovde, who spent 2 1/2 years as undersecretary of the Department of Housing and Urban Development before joining the bank board, said he does not know where he will be working, but probably will be involved with real estate.

Hovde said he is not planning to join any of the 12 regional Federal Home Loan Banks, but did not rule out the possibility of joining a thrift institution.

Gray said he believes Grigsby is resigning to return to Houston but has no specific work plans.

During the last five years, deregulation and falling real estate prices have put the thrift industry through its toughest period since the 1920s. Record failures of savings and loan institutions have threatened to bankrupt the bank board division that insures S&L deposits up to $100,000.

The bank board, which has been under intense pressure from the industry and from the White House and Congress, last month gave Congress a plan to raise money for the insurance fund. The lawmakers could vote on the bank board's proposal as early as next week.