Emmett W. Cocke shrugged yesterday when asked what happened to the homeless people in Fairfax County after the few church-operated shelters there were closed this spring.

"Some sleep in automobiles," said Cocke, minister of the Mount Vernon United Methodist Church, which operated one of nine shelters in Fairfax last winter. "Some sleep in the woods or under bridges or in abandoned buildings, wherever they can find a dark corner."

On Monday, Fairfax, one of the wealthiest jurisdictions in the nation, decided for the first time to operate two county-run shelters for the homeless. The move would take the burden off churches, but one county supervisor was raising questions yesterday about the program and questioning the need for a year-round shelter.

Mount Vernon District Supervisor T. Farrell Egge, a Republican whose district may be the site of one of the shelters, said the county could cut costs for the shelters and might be able to find a building that could be donated for the program.

"We're not making a Taj Mahal out of this," said Egge. "We're talking about a temporary shelter, a home between homes."

Egge said shelters may not be needed in the summer in Fairfax and said he will urge the county to reassign workers to administer the program, rather than hire new employes. About $237,000 would be spent under the county plan for new workers. Lee District Supervisor Joseph Alexander also said he favors using existing county workers.

Cocke, who showed a reporter a field near his church where some of the homeless sleep, said he has no doubt the county needs the shelters. "They should have done it a long time ago," he said. "Any county this big has people who are in trouble and need help, and there's no reason we should have to send our indigent people over to . . .Washington to receive assistance."

Fairfax plans to use county-owned properties or leased space to run the two 50-bed shelters in the Rte. 1 and Baileys Crossroads areas. The county may consider a third center in the Reston area if demand is sufficient.

The cost of the Fairfax program was put at $596,722 in annual costs plus $150,000 in start-up expenses.

After an initial effort to delay a decision on the program, Egge joined six other supervisors at the County Board meeting Monday in approving the new service.

His vote came after assurances from County Executive J. Hamilton Lambert that costs could be cut later.

The proposal to open county-operated shelters grew out of a controversy last year involving Fairfax churches that provided housing for the homeless in what some county officials considered a violation of local zoning ordinances. The churches finally prevailed in the dispute, and last winter they provided shelter for an average of 80 homeless people every night.

The problem of homelessness in Fairfax has been sharpened by the shortage of low- and moderate-priced housing in the county. A blue-ribbon county committee is scheduled to begin examining housing alternatives for the poor soon.

Most of the homeless in Fairfax are men, and their average age is in the late 20s. About three out of four homeless people who stayed in church shelters last winter were unemployed, according to figures compiled by the county.