When Fairfax County Sheriff James W. Swinson opened the county's new $4.6 million jail in February, he believed he had a facility from which no prisoner could escape.

Now, 11 months later, Swinson is facing a problem he didn't believe possible. He can't seem to keep prisoners from trying to break into his jail*

The problem is that both the new Fairfax jail and the state's prison system are overcrowded, so Swinson has had to farm out his prisoners to less crowded jails around Virginia. And that's where the rub begins.

Not only is the Fairfax jail one of the newest in the state, it also happens to be one of the best. Inmates have access to an indoor gym an outdoor exercise area, a barbershop, day rooms with television sets and classrooms with elaborate audio-visual aids for learning new careers.

"Hell, if I was in jail, I would want to be in Fairfax, too," Swinson said this week.

The difference in Fairfax and most county jails in the state is, in the words of Hanover County Sheriff's Lt. T.C. Curtis, "the difference between a Holidaty Inn and a local motel."

So when people confined in the Fairfax jail get sent elsewhere in Virginia-like to Curtis's jail near Richmond-they get angry. "As quick as we get inmates, we farm them out," explains Fairfax's Chief Deputy Sheriff M. Wayne Huggins, "but they know if they make trouble, they will get back here . . . "

Last week Hanover County officials returned an inmate to Fairfax after a fire in his cell, an act the sheriff believes the inmate committed in hopes of getting returned to Fairfax.

Five Fairfax inmates, assigned to the Rockingham County jail in the Shenandoah Valley, were sent home last month after they filed a complaint in federal court about the conditions in the jail there. "I told Fairfax to get them out of here," said Sheriff Weather Holt. "We don't really understand them."

In Dinwiddie County, near the North Carolina line, Fairfax prisoners have begun breaking dishes and throwing "the excellent food we have out here" onto the floor, complains Sheriff Charles L. Mitchell. "We're country folk and these people are city folk . . . They're used to having a lot of money and a good time."

Fairfax prisoners don't even bother to look at the 16-year-old Hanover County jail before complaining, grouses Curtis. "As soon as they walk in the door, before they even sign a paper, they say they want to go back."

All this is making it more difficult to place Fairfax prisoners elsewhere, says Huggins, and "Fairfax is getting a reputation troughout the state as having the rowdiest inmates."

Last week the county had 70 inmates in jails elsewhere in the state, some of them as far away as Gate City in the far southwest corner of Virginia at the Tennessee state line-almost 400 miles from Washington, Huggins said.

Swinson says Fairfax has itself to balme for much of the problem. The new jail was "too small" when it was planned and Swinson said he has argued for years in vain that it needs to be larger.

The new jail is supposed to be able to house 260 inmates, but the deputy sheriffs who run the jail say that figure is deceptive. Ninety cells have to be reserved for juveniles, women and sick inmates, leaving the jail so crowded last week that two classrooms had to be converted into temporary cells with mattresses lining the floor.

Women have had to be placed in cells designed to house men, and last week a "perfectly healthy" woman was placed in a medical room because it contained the only bed available, a deputy said.

"If someone came in right now who was sick," Huggins said at the time, "I don't know where we would move the [healthy] woman."

Under Virginia's corrections system, local jails are supposed to house people awaiting trial and those convicted of minor offenses. The state prison system is supposed to confine persons conveicted of felonies, but there are currently about 1,100 felons awaiting transfer to the state prisons from jails across the state.

"It's a critical situation," concedes state prisons spokesman Wayne J. Farrar. But state officials, he says, have been unable to build new prisons fast enough to keep up with the growing number of people receiving prison sentences.

Some Fairfax County officals have opposed spending more local tax funds for a bigger jail, arguing that the local overcrowding would be solved if Virginia would meet its obligation to house felons now being held in the county jail. Currently the Fairfax jail has 85 people awaiting transfer to Virginia prisons, according to Huggins. That means the county is going to have to continue looking elsewhere for help in housing its inmates.

"At one time we had more Fairfax prisoners here than our own, and they were calling us the Charlottesville Annex [of the Fairfax jail]" said Sam Pruett, manager of a jail in the Virginaia university city. But Pruett said his jail has become so crowded with his own inmates that he is no longer willing to accept prisoners from Fairfax. CAPTION: Picture, Fairfax County's $4.6 million jail, which is having an unwanted surge of popularity among its inmates. By John McDonnell-The Washington Post