The Regan administration has been pressing many of its third World allies to make drastic economic reforms such as those that triggered the recent overthrow of Sudanese President Jaafar Nimeri -- demands that could threaten the survival of other U.S.-backed goverments around the world.

The situation in Sudan was unusual in many ways, but the general pattern was typical: The International Monetary Fund (IMF) and western donor nations, led by the United States, demanded economic austerity and changes to encourage free enterprise. For economic and political reasons, the local government felt that it could not meet these demands, so aid was withheld.Finally, some austerity was imposed, but unrest mounted. In Sudan, unrest led to a military coup.

In recent months there have been signs of similar trouble that put numerous U.S. interests at risk--from the maintenance of key bases in the Philippines to the preservation of latin American democracy to the future of Israel's government and, with it, of Middle East peace efforts.

In easch case, U.S. policy makers have had to grapple with the problems of digging debt-ridden allies out of their economic quagmires without destabilizing their weak governments.

Spurred by such factors as the international debt crisis, the administration increasingly has put an economic and finacial spin on its foreign policy that in many ways has become as controversial as the human rights policies of the Carter administration. Secretary of State George P. Shultz reiterated Regan administration policy recently, declaring that developing countries ''should continue to make the structrual adjustments needed to stabilize their economies, reduct the economic burden of government, expand their trade and stimulate growth.''

In Sudan, Nimeri's downfall came in the midst of demonstrations protesting sharp price increases for food and gasoline that he reluctanly instituted to free nearly $200 million in frozen U.S. aid. There were other factors in Nimeri's downfall; civil war involving religious and separatist differences and the efforts of neighboring Libya's radical leader, Muammar Qaddafi, to exploit them.

Nevertheless, the use of U.S. aid to pressure Nimeri into politically risky economic actions raises questions about the efficacy of American insistence on financial austerity, eliminations of state controls and movement toward free-market economics. These demands have become almost as characteristic of President Regan's foreign policy as his staunch anti-communism.

The philosophy has been given particular emphasis by Shultz, who has steered the administration away from its initial distrust of nonmilitary assistance toward the idea that aid can be a potent weapon in overhauling the world economic order.

In speeches and congressional testimony, Shultz has been a tireless critic of governments that rely ''too heavily on state controls that have deadened the initiative of the small-scale farmers and businessmen who are the backbone'' of Third World economies.

This attitude also prevails in the IMF and the World Bank. Washington and the two principal multinational lending institutions have worked together in pressing recipient countries to end such pracitces as subsidizing the prices of food and other consumer staples, and to stake their economic futures on private enterprise.

Increasingly, however, the administration has found that such a course carries the kind of built-in risks that exploded in Sudan.

''We ask [the leaders of affected countries] to do things that may be politically destabilizing, that in fact may almost ensure their destruction,'' a senior State Department official said. ''Yet, when you look at what needs to be done, there's no choice.''

In the Philippines, where the United States has important military bases, U.S. demands could threaten the ability of an unpopular government to combat a communist insurgency. American economic demands pose a threat to U.S. strategy in Central America by making a weak civilian government in Honduras more susceptible to a rightist military coup and the civilian government in Costa Rica more vulnerable to potential leftist subversion from neighboring Nicaragua.

In South America, the democratic revival praised so strongly by the administration has been dramatized most symbolically by the end of military rule in Brazil and Argentina. But both countries recently were cut off from IMF financial aid because domestic political pressures forced them to abandon unpopular reform agreements.

That has raised new questions about whether their fledgling civilian governments can strike new deals with the IMF that will avert cycles of unrest and military coup. And without the IMF's blessing, neither government is likely to be able to reschedule its huge debts with private banks.

In Peru, however, Alan Garcia, the overwhelming victor in his country's first round of presidential balloting, said he will bypass the IMF and work with other Latin American countries to seek new terms for outstanding commercial loans.

Even in Israel, there is growing concern that if the United States pushes too hard and too fast for major structural reforms, a rising tide of popular discontent could sweep aside that country's traditional U.S.-oriented leadership in favor of a hard-line government whose attitude toward the Arab world would scuttle hopes of resolving the Arab-Israeli conflict.

The results of the kind of economic reform pushed by the Reagan administration have not been clear-cut. The administration cites as successes such countries as Mexico, Zaire and Somalia. But Sudan was a major failure.

Elsewhere, whether in IMF client countries like Brazil, which is the developing world's largest debtor, or in Israel, where the United States is using its aid leverage much as the IMF does in the Third World, it is too early to tell where the pressures for major structural reform will lead.

In the past, the Third World has focused its criticism on the IMF. Sally A. Shelton, U.S. ambassador to the small states of the Caribbean in the Carter administration and now a vice president at New York's Bankers Trust, said the IMF has acted as "the heavy" in forcing debt-burdened nations to confront problems that are at least partly of their own making.

"These countries have to make economic reforms. If they don't do it now, they will be facing even greater disasters down the road," she said. "If they can't meet their debt obligations, the private international banks will not lend them money, suppliers will not give them credit, and they eventually will find themselves in the kind of chaos and paralysis where government cannot function."

The problem with the IMF approach, Shelton said, "is not that it is trying to force reforms but that it too often insists on them being made within unrealistically short time frames that greatly increase the political difficulties."

The situation in sub-Saharan Africa, where at least 28 countries have been forced to borrow from the IMF in the past five years, is widely acknowledged to be especially grim. A recent Central Intelligence Agency report said that although many African leaders are aware that reforms are imperative, they are holding back for fear of being toppled.

A year ago, bloody riots broke out in the Dominican Republic when the government devalued the currency, doubled some food prices and tripled prices of many imported goods. The United States had held up about $80 million in much-needed aid to force the Dominican government to buckle to IMF demands for stringent economic reforms.

In January, the worst rioting in more than four years swept Jamaica in protest against fuel price increases imposed by Prime Minister Edward Seaga as part of a program to undo the socialist-oriented policies of his predecessor, Michael Manley.

Last year, the United States held up economic support funds for Honduras and Costa Rica to force unpopular currency and banking reforms. In Honduras, this increased strains that have led some powerful segments of the military to question close ties with Washington. In Costa Rica, there was widespread denunciation of U.S. interference in domestic affairs.

Sudan was almost a textbook example of the dilemma the administration, the IMF and the recipient country face in trying to cope with huge foreign debt and long overdue economic reforms.

The Sudanese government had fallen more than $100 million in arrears on its repayments to the IMF, halted the economic reforms it had agreed upon last June and was desperately short of foreign exchange.

Because of the arrears, the IMF stopped its aid, and the rescue package put together by western donors last June fell apart.

The U.S. government, the leading western donor, halted a portion of its promised economic support funds -- $120 million for fiscal 1984 and $114 million this year -- because, in the absence of a coherent international program, it would be like "pouring money down a rat hole," as one U.S. official put it.

Sudan's ambassador to Washington, Omer Salih Eissa, talked of his government's dilemma under the intense U.S. and IMF pressure in an interview with The Washington Post a month before Nimeri's fall.

"The aid from western donors was not flowing," he said. "The Sudan was down to rationing gasoline to two liters a week trying to meet IMF demands.

"Do you pay the IMF back or buy gas for your country?" he asked. "Where do we get the money from unless we suspend all imports into the country?

"I really question whether African countries can continue to meet the set of conditions put forth by the IMF," he added.