Virginia officials have agreed to pay "substantial" damages to a 16-year-old youth who was sodomized in the Prince William County jail last year. But lawyers for the state and the youth's family have signed an agreement not to disclose the amount of money to be paid.

Assistant Attorney General Burnett Miller III, who handled the case for Virginia, refused to discuss why the state sought to keep the amount secret. "I'm not going to discuss the terms of the settlement," Miller said. The agreement was filed and sealed in U.S. District Court in Alexandria last week.

Alvin J. Bronstein, executive director of The National Prison Project, which assisted on the suit, said, "at first the state's lawyers wanted us not to disclose that there had been a settlement. We refused that."

The youth's family wanted to avoid the trauma of a trial and agreed to the state's insistence that the amount be kept secret, Bronstein said. His organization attempts to improve conditions for prisoners across the nation through litigation.

"We expect the news of this settlement to have an impact on jailers and prision officials throughout the country," he said. "This was a substantial amount. The case puts jailers and sheriffs on notice that they must develop a system for protecting people in their custody and that they will be held personally accountable if they fail to do so."

The damages were awarded against Jack Davis, former director of the Virginia Department of Corrections; Carl A. Rollins, Prince William County sheriff; Ira B. Faidley, chief of probation in Prince William and Bradley Spain, the county's juvenile probation officer.

Last year, Fairfax Sheriff James D. Swinson was found negligent in an adult jail rape and the victim was awarded $50,000 by a jury. That amount was reduced to $20,000 by a U.S. judge and an agreement finally was reached in which Swinson paid $7,500. In that case as well as the Prince William case the damages are covered by state and county liability insurance policies.

The Prince William youth, then 15 and a runaway from home, had been sent to a juvenile facility as a "status offender," meaning that he had committed no offense for which an adult could be tried. He ran away from the juvenile home, stole a car, was caught and ordered to the Prince William County jail in Manassas in November by a juvenile court judge.

According to lawyers for the youth, his parents told the judge the youth would not be safe there.

During the next week the youth was threatened several times with sexual assault by other juveniles in a 10-bed cellblock and on a Saturday, the day before he was attacked, he sent a note to Sheriff Rollins expressing his fears, his lawyers said. Rollins said yesterday he never received any note.

The youth told his mother and sister during Sunday visiting hours that he was afraid, and his mother contacted juvenile probation officers that day seeking help, lawyers said.

No actions were taken and the youth was sodomized that night by two 16-year-olds who were later convicted in the attack.

Yesterday Faidley said the probation officers, partly as a result of this incident, no longer send juveniles to the Prince William jail. Youths now are transported as far as Lunchburg to state juvenile detention facilities, he said. A Prince William juvenile facility is under construction and is scheduled to open in September, 1978.

Sheriff Rollins said, "There is nothing I want to say about that case . . . I don't know how it's going to be settled. It's not going to be my money." Rollins said his jail was built in the 1050s with 31 beds and now has 62 beds. The daily average was 67 prisoners with a peak in the 90s in 1976, he said.

Asked if a similar incident could occur again he said, "It always worries you. When you don't have enough people it's physically impossible to stop these things."