It costs about $60 a ton to ship steel across the Atlantic, yet European producers are able to sell their steel sheet here for the same $350 to $500 a ton that American companies charge, and sometimes for less.

The Americans say this is because the European companies are unfairly subsidized by their governments.

For several years, U.S. companies have stood aside while government officials tried to negotiate peace pacts with the Europeans; the so-called trigger price system of the Carter administration was one such effort. But this fell apart, and now the U.S. companies have turned to the law by filing complaints with the Commerce Department.

One set of complaints could result in so-called countervailing or offsetting duties on European steel, which in some cases would be as high as $250 a ton and would knock some European producers out of the U.S. market. A profferred settlement of this case was rejected by U.S. producers last Friday; the Commerce Department must now announce its decision by Aug. 24.

And today the department is scheduled to issue its preliminary ruling in another case in which some European companies are accused of dumping, or selling their steel here for less than they would sell it at home. This could result in the imposition of further heavy duties on European products.

Trade war may be too strong a term for all this; Commerce Secretary Malcolm Baldrige prefers the term "family squabble." But steel is plainly one of the leading issues in the current frosty relations between the United States and Europe.

Those relations are intricate, partly because the 10-member European Economic Community and the United States are each other's largest markets as well as leading competitors. The EEC and the United States had $92.1 billion in trade last year. They sold the United States $41.5 billion in goods. The largest categories were petroleum, $6.1 billion; motor vehicles, $4.9 billion; steel products, $3.4 billion; alcoholic beverages, $1.7 billion, and aircraft parts, $1.4 billion.

The United States sold them $50.6 billion in products, including $4.5 billion in office machinery; $3.6 billion in aircraft and parts; $3.1 billion in soybeans and other oil seeds, and $2.4 billion in coal.

There have been skirmishes in several of these areas, such as the one in the commercial airline market between Boeing Corp. and Airbus Industrie, owned by a conglomerate of subsidized EEC companies. There also have been fights over agricultural products.

But the basic battle is over the basic industry: steel. The problem is simply that in a period of recession, world steelmaking capacity is greater than steel demand. The question, as much political as economic, is whose plants and workers are to be idled.

The Europeans, defending themselves against the complaints of U.S. producers, say that American officials are reading U.S. law too narrowly and should be willing to help out old friends who are suffering particularly hard times right now. Besides, they say, the U.S. government helps its industries, too, through special kinds of tax forgiveness and grants, so the Europeans should be able to help their own ailing industries.

And if the U.S. government takes any action against the beleaguered European steel producers, European leaders have threatened to retaliate against imports of American farm products and other goods. Congress, in the midst of an election year with the worst unemployment in 30 years, has warned of its own retribution against the Europeans.

The labor side of the problem may be the most serious.

In 1974 there were nearly 800,000 European steelmakers at work. Now that figure is 567,500 and falling, according to the Commerce Department. The United Kingdom alone went from 197,700 steelworkers eight years ago to 93,600 last year.

In the United States, average steel mill employment dropped from 512,000 in 1974 to 391,000 last year.

Steelmaking in the United States is a $60.1 billion a year business, which last year shipped customers 87 million tons of finished products. Of that figure, 13.2 million tons went to the automotive industry and 11.7 million tons to construction.

But big and basic as it still is, the steel industry is not as big as it used to be. In 1973, steel companies shipped 111.4 million tons of steel of which 23.2 million went to Detroit and 17.2 million went to construction.

After World War II the United States was the unsurpassed leader in steel production. But more recently, younger countries, such as South Korea, have emerged with newer, more efficient steelmaking facilities and workers who are paid low wages. U.S. steel companies are having to spend millions to modernize mills while their workers are paid almost $23 an hour--against $11 an hour for the average U.S. manufacturing worker--making them the highest-paid manufacturing workers in the world. Nine years ago the average steelworker was paid $7.68 an hour.

European steelmakers are also facing increasing worldwide competition and slow demand at home. To prevent large-scale reductions and closings at some of the old steel mills of Europe, and to keep their prices competitive, the European governments allegedly support them with large amounts of cash. The British government, for example, was found by the Commerce Department to have subsidized the price of some steel products made by British Steel by as much as 40 percent.

As the fortunes of European steelmakers have declined, their exports to the United States, the world's largest market, have swelled. Imports contributed only about 2 percent of the supply of steel here in the 1950s, 9 percent in the 1960s and 13.5 percent by 1975 Europe contributed 4.3 percent of that. So far this year imports have climbed to about 23 percent with 6.4 percent of that coming from Europe.

The steel crisis may subside, but the problem probably will not disappear, largely because of worldwide competition. Government studies show employment will continue to decline, and Baldrige said the industry will have to cope with difficult structural changes to survive the international challenge.

Five or 10 years from now, "We won't see the same face on the steel, auto and housing industries that we've seen in the past," Baldrige said. "The problem with the steel industry is international competitors have been modernizing, putting in new plants." Productivity growth in the steel industry has also lagged behind its foreign competition, Baldrige said.

"We have been shocked out of our complacency and smugness," said U.S. Steel Corp. Chairman David M. Roderick. "We now realize that American industry has no manifest destiny to be always first, always right, always best. A world economy includes us, but we are no longer the majority stockholder."