Steel is a sick industry throughout most of the Western industrial world.

The European Community will be producing less steel by the end of the year than it did 30 years ago. America's steel mills, which operated at about 80 percent of capacity last year, are dawdling along with furnaces working at about half speed. Production has gone steadily downhill since March of 1981, when it ran at 88.6 percent of capacity; by last August -- the last month for which figures are available -- the recession had brought it down to 42.4 percent of capacity.

Even the modernized Japanese steel mills face a declining demand for their product. Operating at about 60 percent of capacity, Japanese mills have seen production in the six months that ended in September fall to the lowest level since 1972.

And all of these countries have major problems with unemployed workers demanding rescue operations, often in the form of trade restrictions, from their governments.

The steel mills of the world, the symbols of the industrial revolution, face deep-seated problems that go beyond the current global recession. These problems revolve around the overbuilding of steel-making capacity in the face of a declining market in industrialized nations.

Third World states, meanwhile, are beginning to take care of their own expanding steel needs, while those that have graduated to the status of newly industrialized countries now compete for export markets.

Analyzing those trends, a July study by the Department of Commerce forecast U.S. steel demand would crawl ahead at between one and 1 1/2 percent a year in the 1980s, a higher growth rate than in the 1970s but a slower pace than in the two preceding decades. Demand in the rest of the Western world was predicted to grow at a rate ranging from one to 2 1/4 percent a year, compared with the no-growth rate of the '70s.

The only real expansion in demand for steel was forecast for the less-developed nations. While they had a predicted growth rate of 6 percent a year, the Commerce study foresaw their maturing steel industries meeting their own needs. Futhermore, countries with low labor costs such as South Korea, Brazil and Mexico, were seen as likely soon to become the stiffest competitors to the United States, West Germany and Japan for the world markets.

Recognizing those trends, Frederick Jaicks, president of Inland Steel Co. of Chicago and the chairman of the International Iron and Steel Institute, calls 1982 the worst year in memory for the steel industry. He said profits would be virtually nonexistent for most companies in the world, including his own, which would be in the red for the first time in 50 years.

He predicts that Western steel consumption will drop 8 percent this year, to 379 million tons. Lenhard Holschub, the institute's secretary general, adds his gloomy forecast that U.S. consumption will be off 14 percent to its lowest level in two decades.

What this means, industry analysts say, is that the world's steel companies are fighting each other to hold fast to a piece of the declining global steel pie, which leads to cutthroat competition for export business and a rising tide of protectionism to lock up domestic markets.

A 1981 study by the U.S. Congress' Office of Technology Assessment found that excess capacity in the world steel market results in increased incentives for producers to cut export prices and "dump" steel -- sell it below cost -- while keeping domestic prices high.

The protectionist trend was strong over the past 11 months as U.S. steelmakers fought imports from European competitors by charging them with moving unfairly into the U.S. market through government subsidies or by dumping their product here. This major trade dispute was finally settled Thursday with an agreement reached just in time to avoid punitive American tariffs on European steel imports. That agreement limits the amount of Common Market steel coming here.

While the European Community's industry commissioner, Etienne Davignon, hailed the quota agreement as being "in the best interest of all steel producers," representatives of Europe's steel companies called for similar actions by the U.S. government against other steel exporting nations.

"We hope that Washington will pay the same attention to imports from other sources as it has to those from the European Community because they have just as much effect on the American market," said John C. L. Donaldson, director of the Washington information office of EUROFER, producer organization of the Confederation of European Coal and Steel Community.

The chairman of America's biggest steel company, U.S. Steel, appears heading in just that direction. David M. Roderick, commenting that the agreement with the Europeans "merely transfers problems from one hemisphere to another," suggests that his giant company will file a trade complaint against the Japanese with the U.S. government by the end of the month.

But most independent experts say these protectionist moves will not help steel companies here or overseas overcome their problems of overcapacity and a need to modernize their plants. In the United States alone, estimates a 1981 study by Congress' technology office, the steel industry faces modernization costs of $3 billion a year for the next decade.

Moreover, new trends in manufacture require less steel, indicating a continuing drop in demand. Cars, for instance, are now made of lighter weight steel and substitute materials such as plastics and aluminum as a fuel economy measure. This means a 32 percent decrease in steel use by the automotive industry by 1985, the Department of Transportation reported in a study last year.

Not only is less steel used in new cars, but the decline in U.S. auto production, because of the influx of imported cars, has added to the woes of the domestic steel industry.

Beyond that the steady decrease of steel production over the past 18 months mirrors the effects of the recession. Steel is especially vulnerable to economic downturns since capital goods account for two thirds of its use. Further, the construction industry, devastated by the current recession, is one of the major users of steel products.

The reasons for the Japanese downturn in steel use is similar to the American experience. The economy there is faltering, growing this year at a rate of 3.4 percent instead of the expected 5.2 percent; exports are off; construction is down, and cars are using less steel.

Furthermore, Japan fears the limits on European exports to the United States will intensify competition for sales in key countries, chiefly in the Middle East and Southeast Asia, as Common Market nations slash prices to gain a foothold in those markets. Foreign trade is especially important to Japan, which exports about one-third of its annual steel output.

U.S. steelmakers complain that high wages -- averaging $25 an hour according to industry sources -- raise the price of the U.S. product to uncompetitive levels. Robert W. Crandall, in a Brookings Institute study called "The U.S. Steel Industry in Recurrent Crisis," called this "the biggest problem."

But worries about high wages are not confined to the United States. In Japan, where steel workers make about $10 an hour, there are fears that South Korean steel will invade the market because wages there are far lower -- about $2.50 an hour. In fact, Korea exports more than one million tons a year to Japan.

Korea exports about 40 percent of its annual output of 6.12 million tons, about one-fourth to the U.S.

What this all points to, then, is continuing trade squabbles that are expected to last at least until the worldwide recession abates. While in boom times steel makers manage to find enough markets to keep them all happy, they appear to feel the pinch extremely hard in a slack economy.

Quotas, restrictions and tariffs by one nation, though, almost invariably lead to retaliatory actions and the eruption of a full-scale trade war that no one really wins.