The Carter administration is readying a plan to shorup the ailing Social Security system and make sure it survives its so-called short-term financing problem over the next 10 years.

Then further and more fundamental steps would be required.

Carter aides say their plan will be sent to Congress this spring. Congress must take at least some stopgap action on Social before the end of next year.

That is because the smallest of the Social Security trust or reserve funds - the one that pays benefits to disabled workers and their dependents, 4.6 million people at last count - will run out of money in 1979 if left to itself. Benefit payments are outrunning the portion of Social Security tax collections set aside by law for the disability fund, so the fund is dwindling.

The largest of the trust funds - the one that supports retired workers and their dependents, and survivors of workers who die - will run dry in the early 1980s if left unattended.This fund is now paying benefits each month to 28.3 million people, or roughly one American out of every eight.

No decision has been made on how to raise the money to replenish these funds. But participants say that certain alternatives have pretty well been ruled out.

First, it appears unlikely the administration will propose any increase in the Social Security tax rate, beyond an increase already scheduled to take effect Jan. 1 of next year. The rate is now 5.85 per cent for both employee and employer, and is set by law to rise to 6.05 per cent in 1978. That increase is not intended to be diverted to the disability or retirement and survivor trust funds, however; it is supposed to be for Medicare, which is also financed out of the Social Security tax.

President Ford last year, and again in the fiscal 1978 budget he sent of Congress just before he left office in January, proposed that there be a replenish-the-trust-funds increase in the Social Security rate in 1978, in addition to the scheduled Medicare increase. But President Carter knocked out this proposal in revising the Ford budget - and Carter last year, as a candidate, said he opposed solving Social Security's problems by further increases in the rate.

A rate increase would be regressive, the candidate said, a relatively greater burden for low-wage workers and "the average wage-earner" to bear than for those at higher levels. Therefore, "if additional revenues are needed, I would prefer a more progressive plan to increase gradually the maximum amount of earnings subject to the Social Security tax," Carter said in the campaign.

But administration experts say there are certain problems with this approach as well.

The maximum amount of earnings subject to the Social Security tax is called the Social Security wage base. Under the law, the base is increased automatically each year by about the same percentage that wages rise generally in the economy. These increases in the base are supposed to finance the automatic increases each year in benefit levels; benefits are tied by law to the cost of living as measured by the consumer price index.

The wage base last year was the first $15,300 of each covered worker's earnings. This year it is $16,500; next year it is projected to be $17,700, and in 1979, $19,200.

There are two problems with increasing it faster than this. This first is that the President's economists want to avoid any unscheduled tax increase then, to avoid slowing down the economy. The administration now is nursing through Congress proposals for a cut in taxes - income taxes - this year and next to stimulate the economy.

Second, the experts say there is a limit to what can be gained from an accelerated increase in the wage base, and such an increase also entails an eventual increase in costs.

About 85 per cent of all workers covered by Social Security already have all their earnings taxed; they earn less than the wage base. There is thus not as much money left to be taxed as is sometimes suggested. In addition, the way the system now works, the higher a worker's taxed wages, the higher the ultimate benefits.

Still, a wage base increase could help, at least in the short term. The AFL-CIO wants to raise the base until about 95 per cent of all covered workers have all their wages taxed. (Then it would continue to rise from that point each year with inflation).

Social Security actuaries say that, for 1979, it would take a wage base of about $27,600 to cover all the wages of 95 per cent of all workers in the system. Raising the base that far beyond present plans would produce an additional $9.6 billion in revenue that year, they estimate.

With that kind of infusion, the old-age, survivors and disability funds would build back up for a while. By the late 1980s, however, for demographic and other reasons, they would start dwindling again and need additional strengthening.

But administration experts - most of the work on the issue is currently being done inside the Department of Health Education and Welfare, which administers Social Security - note that increases in the Social Security tax rate or base are not the only way to solve the system's short-term problem.

One alternative is to take some of the money now earmarked for Medicare and shift it into the disability and other non-medical trust funds. For the short run, at least, the Medicare trust fund is said to be in relatively decent shape, and could withstand such a transfer.

The other alternative would be to pay some Social Security costs out of general revenues or income tax receipts.

That would be highly controversial, Traditionalists say it would destroy the basic idea of Social Security - that workers earn their benefits through "contribution". But others say this earned benefit idea has always been a myth - that Social Security has never been more than an annual transfer of some income from the self-supporting part of the population to those parts no longer able to support themselves. If that is true, use of the income rather than Social Security tax makes no difference.

The administration's decision on these financing questions may come with the annual report of the Social Security trustees - the secretaries of Treasury, Labor and HEW. That report will be made to Congress next month.