The Reagan administration's policy of encouraging the owners of commercial ships to build and overhaul their vessels in foreign yards has hit hard at one of the most depressed U.S. shipyards, Bethlehem Steel's unit at Sparrows Point in Baltimore. It cost Bethlehem a major order and, without new work, the yard may face closing, company officials say.

A $100 million rebuilding job on six freighters owned by Delta Steamship Co. of New Orleans that probably would have been done in Baltimore under rules that prevailed from 1936 until last year is going to be done instead in Scotland, according to officials of Bethlehem and Delta.

A Bethlehem spokesman said the workforce at the Baltimore shipyard has dwindled to about 400 persons. David H. Klinges, Bethlehem Steel's vice president for shipbuilding, said the company is "hungry for work," and if it is not selected to do one of four U.S. Navy jobs on which it has bid, "we disappear."

Delta is one of eight U.S. merchant marine companies that receive federal subsidies for operation of ships in international commerce. Until last year, the law required that subsidized operators use only ships built and overhauled in U.S. yards. The construction work also was subsidized because foreign yards are cheaper.

The Reagan administration, with the consent of Congress, eliminated the construction subsidies, which in the 1980 fiscal year cost $265 million. Loss of construction subsidies would have made it very difficult for the ship operators to undertake the vessel replacement and overhauls required by their operating subsidy agreements, so the new rules authorized them to go to foreign yards for the construction work formerly done in the United States.

Delta, which is overhauling and enlarging six ships used on its South American routes, rejected Bethlehem's bid and is negotiating with Tyne Shipyards in Great Britain, Delta officials said. They said no contract has been signed, but it is clear that even if Tyne is not selected some other foreign yard will get the contract, maritime industry sources said.

"Delta had no choice," said Klinges.

Bethlehem, which once employed about 3,000 skilled shipbuilders, now has "nothing under contract," Klinges said.