When it comes to pushing "Star Wars" to the public, industry has taken a back seat to the White House and adopted a soft-sell, behind-the-scenes strategy.

Big profits, of course, would depend on the manufacture of actual hardware. But government research funding already has made the Strategic Defense Initiative, known informally as "Star Wars," something of a fixture in America's defense-industrial economy.Corporations are quick to point out that "Star Wars" has little impact on their overall business right now. Nonetheless, in fiscal 1988 about $4 billion flowed to several hundred contractors in at least 35 states and several foreign nations.

Many times that amount and thousands of jobs are riding on eventual deployment of a shield against ballistic missiles; therefore, many leading defense contractors have gotten in on the ground floor of "Star Wars."

According to the Federation of American Scientists, the top 10 corporate recipients of "Star Wars" funding during the fiscal years 1983 through 1988 were: Lockheed Corp., $1.65 billion; Hughes Aircraft Co., $881.1 million; TRW Inc., $778.9 million; Boeing Co., $757.6 million; Rockwell International Corp., $701.1 million; McDonnell Douglas Corp., $647.5 million; General Electric Co., $578.1 million; Martin Marietta Corp., $514.1 million; Teledyne Inc., $411.7 million;and EG&G Inc., $387.6 million.

As for geographic distribution of "Star Wars" spending, California leads the nation, followed by Massachusetts, Alabama, Washington, New Mexico, New York and Maryland, according to the Strategic Defense Initiative Organization. Rounding out the top 10 states are Virginia, Colorado and Texas.

Worried that a heavy-handed marketing campaign could backfire, the big corporate players have kept a low profile so far.

Since the most lucrative production contracts are years away, "Star Wars" has yet to develop the kind of political and industrial clout that propelled the controversial B-1B strategic bomber into production.

"I can't think of any of the aerospace contractors who have gone out and attempted to influence public opinion," says Michael Gamble, manager of strategic defense programs at Boeing.

"We don't want to . . . meddle, or foul up what the government wants to do," says Michael Yarymovych, vice president and associate director of Rockwell's Strategic Defense Center.

The program's toughest critics say that that industry has let the Reagan administration take most of the political heat for the controversial program.

"In many respects, (companies) are taking an intentionally low profile to avoid public controversy," says John Pike, associate director for space policy at the Federation of American Scientists and a longtime opponent of SDI. "One way to avoid controversy is to not blow your own horn."

Companies can afford to do that right now, since "Star Wars" is still a small part of the total pie for most defense contractors.

It accounts for "less than 3 or 4 percent" of their revenues, says Phil Friedman, a vice president for research at the investment company of Drexel Burnham Lambert.

"There are very few `pure players' in SDI" - companies solely dependent on "Star Wars" work, Friedman says.

The major corporations involved in "Star Wars" work say that the program is an important, but small, part of their overall business.

For example, Martin Marietta, with $514.1 million in SDI work so far, had sales of $5.2 billion last year. General Electric, ranked sixth in the Fortune 500 list of largest U.S. industrial companies, has received $578.1 million in "Star Wars" money since 1983. Its revenues last year: $40.5 billion.

In addition, the number of jobs tied to SDI is similarly small. The aerospace industry as a whole had a work force of 1.3 million last year. But SDI accounts for just a few hundred workers at many of the top contractors, themselves industry giants.

At Boeing, for example, the program accounts for "somewhere under 1,000 people at any given . . . time," out of a work force of 100,000, according to an official. "It's less than 1 percent of our employment total."

TRW has a higher portion of its workers on the program, about 1,400 out of 30,000. But in terms of total business, SDI accounts for only 2 to 3 percent, says SDI chief Bernie Lubarsky. "It is not, percentagewise, a big item."

There has been no attempt to build a political base for "Star Wars" through contracting, insists Col. Nicholas W. Kuzemka, contracts chief for the Strategic Defense Initiative Organization.

"We have been very concerned about those kinds of criticisms," he says. "This is such a political program. You don't want to give additional ammunition to the folks on the other side."

SDI is a sophisticated "system of systems," he says. That means contracts naturally flow to states noted for their high-tech and defense work and to the big defense companies that compete for the work.

Wall Street analysts point out that all of the "Star Wars" work is research and development at this point, where profits are typically lower than in actual weapons production.

"It's really not significant in terms of the bottom line because it's not profit," says Gary Reich, an aerospace analyst with Shearson Lehman Hutton.

That is not to say that industry doesn't care about the program.

With at least $16.7 billion in federal research and development money already spent, "Star Wars" represents the nation's biggest technological push since the golden era of the space program.

"For missile and space companies, what else are they going to do?" asks American Scientists' Pike. "There's nothing else in the pipeline."

Privately, companies are scrambling for their pieces of the pie.

Their efforts have included slick marketing brochures displaying exotic anti-missile weapons, such as the space-based lasers and anti-missile rockets housed in high-tech orbiting garages.

Such companies as Martin Marietta, Rockwell, McDonnell Douglas and General Electric attend trade shows displaying their wares.

They make their views known through specialized trade groups, such as the Aerospace Industries Association.

Private groups also get involved.

The American Defense Preparedness Association, a Washington-based group boosting military readiness, makes available a flashy audiovisual presentation telling how the "Star Wars" system might work. The High Frontier organization, headed by Gen. Daniel Graham, was a seminal advocate for a space-based missile defense system.

And the contractors themselves brief members of Congress looking for information on the program - both at the members' request and on their own.

Although they have not been aggressive in taking their case to the public, SDI contractors apparently have been less restrained in lobbying Congress on the program.

According to a report by the New York-based Council on Economic Priorities, "SDI money is already talking on Capitol Hill."

The group found that from 1983 through spring 1986, $6 million was given to candidates for federal office by the political action committees of 16 of the 20 companies with "Star Wars" work.

In the House, members of two crucial committees with influence on the "Star Wars" budget got 35 percent of the PAC money. Members of corresponding committees in the Senate pulled in 56 percent of the PAC money, the group found.

Why so much attention to a program that companies say has a marginal impact on their bottom lines right now?

"It's not a big sales issue at this stage of the game," says Morris H. Thorson, vice president for SDI at Martin Marietta Astronautics Group. "However, the technology is extremely important to us. We are working on the leading edge of technology in the SDI area."

But, if a "Star Wars" system is ever deployed, he says, "that would be very big business."

At its 12,000-worker plant in the Rocky Mountain foothills near Denver, Martin Marietta is building the 100,000-pound Zenith Star, a space-based laser weapon intended to zap enemy missiles while they are still rising into the atmosphere.

Under a separate $142 million contract, the company is competing with Rockwell International to build the Space-Based Interceptor. That system of sophisticated rockets would ride in orbiting "garages" high above the Earth, poised to smash into attacking missiles long before their deadly descent.

In Colorado Springs, meanwhile, the company is building a 550,000-square-foot complex, the nerve center of a sophisticated computer network to simulate a working "Star Wars" system.

The $508 million National Test Bed contract (the largest awarded under the SDI program so far) currently employs 600 people and is intended to serve as the nerve center of a system spanning the country.

Says Thorson: "Research efforts are normally a means to an end; it's to build a base."