The nation is pouring an ever-larger share of its health spending into care of the elderly, new government figures show.

Although persons 65 and over made up only 11 percent of the population in 1977, they accounted for 29 percent of all public and private health spending, up by one-quarter from a decade earlier.

For elderly persons, average health care cost in 1977 was $1,745 compared with $661 for persons 19-64 and only $253 for the young.

The figures, compiled by the Department of Health, Education and Welfare, reflect the increase in the aged population, which is growing faster than other age groups and the special needs of older persons who suffer chronic conditions and are hospitalized or sent to nursing homes more frequently and for longer periods than the younger population.

They also reflect the fact that special programs like Medicare are available to the elderly to pay for part of their costs. Lacking these programs, individuals might fail to seek treatment and their proportion of national health spending would be lower.

The HEW survey shows that $142.6 billion was spent on health care by all public and private sources in 1977 -- $18 billion on the young, $83 billion on those 19-64 and $41 billion on the elderly.

The elderly were by far the biggest beneficiaries of government programs. Overall, $57 billion of total health spending for all groups came from government sources and nearly $28 billion of this went for the elderly -- largely for nursing home care, hospital care and physicians' services under Medicare and Medicaid.

However, even though they got nearly $28 billion of their bills paid by government, the elderly still had to pay another $13 billion from private health insurance or out of their pockets. Thus, about two-thirds of health spending on the elderly was paid for by government.

For other age groups, the proportion was roughly reversed -- two-thirds of outlays came from private sources and only one-third from government.

The high proportion of spending -- and especially government spending -- on health of the elderly reflects one aspect of what many have called "the crisis of aging" in America. At one end, the birthrate is declining. At the other, people are living longer.

This means that the number of young, active workers available to support the retired and ill population is declining. Each younger worker may eventually have to pay an everlarger share of his or her income to help support the growing needs of the elderly. That fact is what underlines some of the financial problems of public retirement and health systems and is helping to fuel what is being described as the taxpayers' revolt.