Engineers quickly buttressed the sagging roof at Wolf Trap's Filene Center last week when a gaping crack was discovered in one of four main structural beams. That was the easy part.

Now comes the hard part: Figuring out which of the contractors is at fault, and whose insurance company will foot a repair bill that could run to hundreds of thousands of dollars.

Officials of the various contracting companies that might be found at fault have called on experts at Lehigh University in Bethlehem, Pa., to determine the cause of the fissure.

Yesterday, workers cut two U-shaped hunks of steel from either side of the 2-inch-wide crack to send to the university, where they will be tested. Repair work will not start until the cause has been determined.

Although officials say it is unlikely, squabbles over who will pay the center's repair bill could conceivably delay the work and postpone the opening of the 1985 season, tentatively scheduled for June 8.

"I think all the parties are worried," said A. Russell Versaci, project manager for Dewberry & Davis, the Fairfax County firm that designed the $18 million structure. "It's going to be messy."

The companies involved in rebuilding the center after a 1982 fire -- including Dewberry & Davis, the architect and engineers; Bethlehem Steel of Bethlehem, Pa., the steel supplier; Globe Iron Construction of Norfolk, the beam fabricator, and G&C Construction of Vienna, the chief contractor -- agreed last week to turn the investigation into what caused the fissure over to John W. Fisher, a professor at Lehigh and an authority on material fatigue and fracture.

"We decided it was better to cooperate and give it to Lehigh than to have separate labs doing the same tests," Versaci said.

"I think the worry by all the parties is, 'Is it our fault? Is it partially our fault? Is it not our fault?' It's just an onus," Versaci said.

In a meeting last week to decide who would conduct the tests to determine the cause of the crack, several representatives of the companies involved questioned the impartiality of Lehigh, which has close ties to Bethlehem Steel -- the supplier of the steel in the beam, according to several participants. They ultimately decided that Fisher was "beyond reproach," according to one participant in the session.

Fisher could not be reached for comment yesterday.

Versaci said it will take at least two weeks to determine the cause and it is likely Fisher's report will point to multiple causes for the fracture, including the extremely cold weather about the time it was discovered. After that, it will be up to the insurance companies for the various contractors to work out who will pay and how much. Arbitration and lawsuits are possible, according to one source close to the process.

"What's going to come out of the report by Fisher is going to be more confusion," Versaci said.

The fissure, discovered Jan. 24, runs vertically along three sides of a 138-foot-long steel beam. The Filene Center reopened last June in Wolf Trap Farm Park, the first national park in the country devoted to the performing arts.

The roof is now bolstered by more than a half-dozen towers of scaffolding, which replaced a steel sling that was originally suspended from a crane to support the roof.