The U.S. steel industry, struggling with its own strain of the import virus, is reaching for some of the same medicine administered to the auto industry.

Behind the steel industry's barrage of unfair trade suits aimed at foreign competitors is a demand for relief from lower-priced steel that is pulling much of the profit out of steel-making operations in this country.

Like the auto industry, steel says that it is embarked on a major investment campaign to modernize plants, making them more competitive against products from Japan and other countries with lower labor costs and more efficient processes.

In a little over a year, U.S. steel producers have announced plans to build $6.1 billion in new facilities by the mid-1980s, on top of normal investments in their plants, according to the American Iron and Steel Institute.

The announced projects represent a doubling of investments in modernization of steel-making facilities, the AISI says -- the kind of response that President Reagan is counting on as the payoff from the huge tax cuts given to business in last year's economic program.

But steel producers are warning that they won't meet that investment goal unless their profits improve.

"The whole modernization program is jeopardized by these imports," says Bethlehem Steel Corp. Chairman Donald Trautlein.

"If we can't make those investments, the industry has nowhere to go but down," Inland Steel Co. Chairman Frederick G. Jaicks said in an interview late last year.

To be profitable, the industry must run its plants at high capacity, and imports -- together with the recession -- have dropped operating capacities to 55 percent, from 80 percent last spring. The foreign competitors "are eating our lunch," says Jaicks.

The current profit squeeze in steel-making is particularly painful for Inland, the seventh largest domestic steelmaker, which led the industry both in profits and in a commitment to investment in modern, efficient steel-making technology for many years.

Inland's pride is the No. 7 blast furnace, the largest in the Western Hemisphere, with a computer-run control system that Inland believes is the most advanced in the world.

It went into operation in October 1980, culminating a $1-billion modernization program at Inland's Indiana Harbor Works that began in 1974.

With the new blast furnace contributing to lower operating costs, Inland expected to take a big forward step in its competitive position against U.S. and foreign steelmakers.

Instead, it has been hurt by tumbling demand for steel in the auto industry, a key market, and by the low-cost foreign steel.

The results so far are not what Jaicks had in mind when Inland committed itself to the aggressive capital spending program.

The new blast furnace and other investments are still a mixed blessing at this point, Jaicks said. "In all frankness," he said, "we got ahead of ourselves by adding a million tons of capacity" -- just as the impact of higher oil prices and imports were pushing the domestic auto industry into a long slump.

Inland "misread" the effects of the oil price surges, he adds.

The efficiency of the new blast furnace has lowered Inland's operating costs, Jaicks said, "but not by nearly enough to pay the additional carrying costs" of the debt Inland incurred in building the furnace.

That lesson hasn't been lost on Inland's rivals now facing investment decisions, steel executives say. They want a long-term cure to the pressure of imports. "A five-year breathing spell has been central to discussions between the steel industry" and the administration, said one steel industry source.

The Reagan administration reluctantly arranged a breathing spell for the U.S. automakers last year by pressuring Japan into a two-year limit on car shipments to this country. The auto industry depression has taken the teeth out of that action, holding down sales of Japanese and U.S. cars alike.

There is little chance that the Reagan administration will voluntarily intervene for steel as it did for the auto companies, however, because of the president's desire to maintain credentials as a free trader.

The steel companies hope they won't need direct help, however. The critical difference between the auto and steel situations are the trade actions brought by seven U.S. steel companies against rivals in 11 foreign countries -- including Brazil, South Africa, Romania and most of Western Europe.

They charge the foreign producers with illegal dumping of steel in this country at below-cost prices, made possible by large subsidies from their home governments, also in violation of trade law.

The U.S. steel companies are asking for import duties -- penalties that would raise imported steel prices by $100 a ton or more, closing the gap with competing U.S. prices.

If the steel suits pass initial scrutiny by the Commerce Department and the U.S. International Trade Commission next month and the cases aren't delayed by their complexity, a critical ruling would occur in June, steel officials say.

The steel industry is hoping that Commerce will make a preliminary finding then that its claims of foreign subsidies are true. That would raise a threat of significant penalties on steel shipped from the 11 countries, retroactive to this March -- a prospect that should make import steel brokers think twice about foreign orders, one executive said. A final decision would not come until 1983.

An industry critic who opposes the steel campaign is Robert Crandall, an economist with the Brookings Institution.

There is a similarity between the steel and auto situations, says Crandall, although not the one industry leaders mention.

The U.S. industry is stuck with too many old, inefficient plants and with labor costs that are far too high to meet world competition, according to Crandall.

The protection the steel industry wants would remove any incentive for industry-union compromises on lower costs of the kind now being sought in the auto industry, says Crandall.

And even "givebacks" by the United Steelworkers of America won't make the older plants profitable, he contends. Like the auto industry, steel faces a gradual but steady shrinkage as older plants and mills close, he said.