A wary US mutes publicity for coming economic summit.

So sharp are the trade quarrels among Western allies that the White House is playing down advance publicity about the economic summit to be hosted by President Reagan in Williamsburg, Va., in May.

If the Williamsburg summit is to succeed, says a US official, it must be ''unstructured'' and not focus on interallied disputes over trade.

''My guess,'' says Lawrence B. Krause, an international economist with the Brookings Institution, ''is that if we had not designed a mechanism to have summits every year, we probably would not have one now.''

The purpose of the annual summits, which began at Rambouillet, France, in 1975, is to bring together presidents and prime ministers of seven leading noncommunist nations, plus the president of the European Community (EC) commission, to coordinate economic planning.

Over the years the summits have taken on a life of their own, drawing thousands of bureaucrats and reporters from around the world and throwing a glare of publicity on the West's top leaders.

The problem this year, experts agree, is that all of the summit participants, including President Reagan, will be under extreme pressure to defend national interests, especially where trade is concerned.

No leader can ignore the fact that in Canada, the United States, and Western Europe unemployment is at the highest level since World War II, with little relief in sight.

Cancellation of the Williamsburg summit is out of the question. ''The affair has acquired so much momentum,'' says former State Department official Robert D. Hormats, ''that to cancel it would in itself be a negative.''

Against this background the summit planners - popularly known as ''Sherpas'' because they smooth the way to the mountaintop - struggle for a way to minimize friction and turn the summit to mutual advantage.

''Advance preparation for the summits has become a huge bureaucratic project to the extent that the bureaucracy has structured the summit,'' says Undersecretary of State Allen Wallis, President Reagan's Sherpa.

''The Sherpas have gone to work six months before the summit, saying - 'What should our leaders talk about? How can we use our president or prime minister or chancellor to pull some of our chestnuts out of the fire?' ''

The end result of this process usually is that summit communiques generally are agreed upon and written, before the top leaders arrive on the scene at all.

''By the time they got to the summit,'' says Mr. Wallis, ''the leaders were very much constrained by agreements that already had been worked out.''

This time around, if Reagan has his way, the top leaders will meet as informally as possible, at times without the Sherpas, to talk about fundamental principles and policies.

As an example of the administration's effort to de-emphasize trade differences before the summit, a half-hour videotape, featuring interviews with senior American officials on US summit aims, was abruptly canceled by the White House after production had begun.

The program, scheduled for worldwide distribution but not for showing in the US, necessarily would have included criticisms of trade policies of the EC and Japan.

The summit communique, White House officials hope, will be muted - though not the centerpiece of the summit, since, as Wallis says, there will have to be some communication between the leaders and the press.

Meanwhile, charges of unfair trade practices fly back and forth among the summit powers. The US and EC accuse each other of subsidizing exports to the other's detriment. Japan comes in for a drubbing from Europe and the United States.

So far the presidents and prime ministers have kept pretty much out of the line of fire, letting their cabinet ministers and bureaucrats do the slugging.

''There is something that can be done for the world at Williamsburg,'' says Brookings economist Krause. ''That is to ensure that we have a sustained (economic) recovery. We must have a sustained recovery to reduce these high levels of unemployment that we find in all industrial countries.

''The United States cannot have a recovery alone,'' he says. ''If the economies (of Europe and Japan) do not recover, the US could find its recovery faltering after a year or so. Even the US is not large enough to be the sole island of prosperity in a sea of troubles.''

The task at Williamsburg, he says, is to have the leaders ask themselves: ''Is my country, through my government's policies, participating in a common effort at recovery?''

''At the moment,'' says Krause, ''the interaction of these economies is very strained, because conditions over the last two years have in fact promoted trade disputes and protectionism.''

Attending the Williamsburg summit May 28-30 will be government heads from the US, Canada, Britain, France, West Germany, Italy, Japan, and the president of the EC.