The World Bank, the largest source of development funds for growing and backward economies, faces an unusual predicament: Its cash drawers are overflowing, but borrowers aren't standing in line to get loans.

It is highly embarrassing for the bank, which has been widely challenged to play a more significant role in meeting the existing financial problems of the world, to be sitting atop a pile of money it can't move. It has at least $2 billion budgeted to shovel out in commitments this year for which there are no takers at the moment.

"[Former bank president Robert] McNamara would have spent the money a couple of years in advance," said a development aid expert in half jest.

For the bank's fiscal year that will end June 30, 1985, it now appears that the commitments for new loans will be no more than $11 billion, compared with a range of $12 billion to $13 billion estimated as recently as the annual meeting here in September 1984.

This is the latest problem for the bank's current president, A. W. (Tom) Clausen, who has been hammered unmercifully by a generally disapproving and unfriendly Reagan administration. It will surprise no one in Washington if Clausen, working in the shadow of the more dynamic McNamara, bows out when his five-year term ends in mid-1986.

Clausen has found it difficult to put his own imprint on the bank at a time when there is a widespread perceived need for the bank to adapt to changing economic conditions. The bank persists in stressing "project" loans, which many countries no longer can afford because they can't put up their own required share of the funding.

Instead, as critics have been saying for the past two years, the bank has to do more "program" lending, which allows Third World borrowers more leeway to use the funds -- with less new commitment of their own.

Unless the bank softens its loan criteria, or changes its rule that places limits on the amounts of money individual countries are allowed to borrow, some observers think that the bank's new commitments this year may fall even below the $11 billion estimate. As interest rates settle back somewhat, many countries already have decided to bypass the "hassle" of strict bank conditionality and seek commercial loans instead.

The irony of the situation was underscored this week when the bank reported that it is piling up stunning profits by judicious investment and borrowing techniques. This enhances the bank's triple-A rating in the money markets and strengthens its reserves, but it doesn't do anything to ease Third World debt burdens.

To be sure, the United States -- the bank's biggest shareholder -- has not wanted to see a more liberal lending policy at the bank. So, in large part, Clausen's problems are traceable to the restraints dictated by the Reagan administration, which distrusts all multilateral institutions. The United States at the moment prefers bilateral relationships where it can try to use economic aid as leverage for its own military and diplomatic priorities.

But Clausen has other problems in managing the huge bank bureaucracy. For example, some executive directors complain that Clausen was maladroit in the way he broke the news that because of declining loan demand, his long-discussed proposal for a major increase in the bank's capital had best be put off, at least until the annual meeting in Korea in October.

According to some present, the former chairman of BankAmerica sat through a six-hour executive board discussion of the capital increase at the end of December. Then, with no warning, he dropped his bombshell: Commitments were off by $2 billion, and therefore, he would postpone the formal initiation of a capital increase that had been planned for the April meeting of the IMF/World Bank policy board, the Development Committee. It was the first time the directors had heard of the extent of the decline in borrower demand, and they requested a staff paper be drawn explaining what was happening, to be presented for discussion at the February meeting.

When this news leaked out, bank spokesmen tried to gloss it over by saying there never had been firm plans for a capital increase proposal, which would not be needed to cover the level of loans until the next decade.

It can be argued persuasively -- and it is surely Clausen's position -- that the bank should not throw its money away merely to meet an earlier projection, and that it would be irresponsible to press for a capital increase when the need is not present.

But the fact is that Clausen's original schedule, before the current slippage, projected an annual growth in loan commitments of 5 percent to 10 percent a year, a progression that could not be sustained even in the next couple of years without a capital increase. Moreover, Third World countries insist that at least that much growth in bank lending is needed to reverse their present desperate state of affairs, which finds that more money is flowing from the poor countries to the rich countries than the other way around.

Bank figures show that in 1983, net financial transfers to Third World countries added up to a negative $11 billion -- in other words, interest and other repayments exceeded new loans by that much money. Unofficial estimates put the negative flow at about $7 billion this year.

"The truth," says a bank insider, "is that, except for the U.S., there had been no question about the need for a capital increase. The only debate was about how big the capital increase should be." The amounts discussed ranged from $20 billion to $60 billion; the latter amount would double the existing capital base.

"There's no shortage of need out there in the Third World ," says a development expert, "but the bank has to change its focus in order to meet it."

What the $2 billion shortfall shows is that there no longer is time for the extended debate that goes on internally on the nature of the bank's "role." The need for a dramatic reorientation of priorities at the bank is here and now.