Immediately after World War II, the United Auto Workers outraged corporate America with a demand that General Motors open its books to union inspection.

Walter Reuther, then a vice president of the union, asked for the audit so the UAW could determine how much of a wage increase the company could afford without having to raise the price of its cars to the consumer.

Reuther's demand for a look at the books was immediately denounced by industry as nothing more than socialism, and the UAW was invited to keep its nose out of the free enterprise system. Since then, most unions have done just that. Until now.

In recent months, several companies have granted their unions a look at the corporate books as part of an appeal for contract concessions. Perhaps the biggest corporate move in this area has occurred at Uniroyal where the United Rubber Workers has been given the right to audit the corporation's books to help determine the validity of the company's claims of poverty.

As a result, the URW appears ready to grant Uniroyal $54.9 million in contract concessions over the next three years.

Last month, the major unionized companies in the nation's meatpacking industry agreed to detailed disclosure of capital expenditures at each company plant at the end of each contract year to the United Food and Commercial Workers International Union.

In exchange, the union granted the companies what amounts to a four-year freeze on all wage and cost-of-living increases while they modernized their operations in an attempt to compete with nonunion firms.

Perhaps the biggest disclosure to date involves the Chrysler Corp. As part of the government's $1.2 billion loan guarantee program, Chrysler's books were audited closely by the federal government.

In each case, the union's ability to look at the company books has been a powerful political weapon for union leaders trying to deal rationally with requests for contract concessions. UAW President Douglas Fraser, for example, refused to consider Chrysler's second request for concessions until after the Treasury Department had completed its look at Chrysler's financial records. Only then was Fraser able to go before the union membership with a proposal for more concessions.

Now General Motors and Ford are demanding major contract concessions from the UAW for themselves. GM has been running a massive campaign since fall to try to persuade the UAW membership either to give up contract benefits or to risk losing their jobs. The campaign is accompanied by a flurry of numbers showing how much more expensive American autoworkers are than their Japanese counterparts. Ford has been making similar demands.

And the airlines industry, which already has won major contract concessions from some of its unions, appears headed into rough negotiations with demand for similar concessions from the International Association of Machinists.

Other companies and industries can be expected to join the concession chorus as the year goes on.

Therefore it seems reasonable that any corporation that is serious in its demand for contract concessions from its union workers--concessions that often are demanded without similar concessions from the company's nonunion employes--should be willing to submit its financial records to audit by the unions.

This appears to be the course the truly needy of corporate America have been willing to take.