Northern Virginia has a severe shortage of housing for elderly persons who cannot live independently but do not require nursing-home care, according to a study by the Health Systems Agency of Northern Virginia.

Also, because the elderly are the fastest growing segment of the population, the shortage, "while it is a problem today, could be more of a problem tomorrow," said Mark Epstein, assistant director of the HSA, a regional health planning agency established by Congress.

Fairfax County, one of several jurisdictions that requested the study, already was considering converting the closed Lincolnia Elementary School, near Landmark Shopping Center, into a 54-bed home for low-income adults because of the county's growing need.

The Fairfax County Board of Supervisors has not taken a position on the proposal, but voted yesterday to hold a public hearing on Lincolnia on Jan. 7. County staff members estimate that the renovation of the school would cost about $1 million and yearly operating costs would be about $700,000.

The HSA's report said that hundreds of elderly persons in Northern Virginia need "domiciliary care" facilities where they can get nonmedical services, such as help with bathing, dressing, meals and housekeeping. In addition, many younger people with mental disabilities need adult-care facilities because mental hospitals are keeping them for far shorter periods, the report said.

The problem is particularly acute among the poor, the study found, because Medicare and Medicaid do not pay for such care. Supplemental Security Income and state assistance of up to $586 a month are available, but they are insufficient to cover adult-home fees, which can run from $800 to more than $1,000 a month.

Currently, the only facility low-income persons use in Northern Virginia is The District Home, a 73-bed home in Manassas, run by Prince William, Fairfax, Loudoun, Fauquier and Alexandria.

Thelma Petrilak, a senior supervisor with the Fairfax County Department of Social Services, said the agency often has to place people in adult homes hours away from Northern Virginia, making it difficult for them to see their friends and families. "It's very painful," she said.

In a survey of social workers, hospitals and health-care experts taken by the HSA in July, 370 persons in Northern Virginia were in immediate need of domiciliary care, but were unable to obtain it in the area.

In addition, Goodwin House in Alexandria, which has 329 adult-care beds, has a 300-person waiting list. Leewood Lodge in Fairfax, with 50 adult-care beds, has 15 waiting.

The 15 domiciliary facilities in Northern Virginia house 1,548 persons. The HSA study predicted that 1,500 more such beds will be needed by 1990.