Two-thirds of single elderly people and one-third of married elderly people who enter nursing homes face destitution within 13 weeks because of the high costs of health care, a survey by Blue Cross and Blue Shield of Massachusetts has found.

A summary of the study, which covers people age 66 and above, is to be released today by Rep. Edward R. Roybal (D-Calif.), chairman of the House Committee on Aging.

A companion study by Harvard Medical School's Massachusetts Health Care Panel Survey found that among single people 75 and over, about half would face poverty after 13 weeks in a nursing home.

Both studies concluded that by the end of two years, between 80 percent and 91 percent of elderly people going into nursing homes would be destitute.

In addition, both studies found that for an Alzheimer's disease victim who was married and stayed at home with the family providing care, the cost of home health services would be so great that more than half of the families would be impoverished after two years.

The House panel said that in Massachusetts, where the surveys were conducted using sample families in the community, the rate most frequently charged in a private, skilled nursing facility is $75 a day -- or $27,000 a year.

"The approximate cost of caring for an Alzheimer's victim in the home in the advanced stages of the disease was estimated at $35 a day, or nearly $13,000 per year," the committee said.

Medicare and private insurance policies normally do not pay for long-term nursing home care. But once a person uses up most of his financial assets and his income drops to the state eligibility levels -- often well below the poverty line -- he can become eligible for nursing home support through the state Medicaid program. Almost half of the total outlay under the Medicaid programs go for nursing home care.

The studies released by Roybal underscore the growing concern in the health care community over the costs of long-term nursing home care, particularly as the population ages.

A recent study conducted for the American Association of Retired Persons by ICF Inc., a consulting firm, found that while public programs (mainly Medicaid) in 1986 would provide more than $16.6 billion for such long-term care andapproximately $200 million in private insurance, households with members in nursing homes would have to pay another $16 billion in out-of-pocket expenses. This $16 billion was estimated as the largest out-of-pocket cost for the aged, with drugs second at $7.3 billion.

"The message is clear," Roybal said in a statement attached to the report on the two Massachusetts studies. "The likelihood of impoverishment is extremely high if an elderly person is placed in a nursing home or needs extensive home care on a long-term basis." He said out-of-pocket costs for the elderly should be held below 15 percent of income and a policy should be developed to handle long-term care.