Seventeen major American corporations that together earned $2.6 billion in 1976 paid no U.S. income taxes that year, according to figures compiled by Rep. Charles A. Vanik (D-Ohio).

In addition, 41 other large companies out of 168 surveyed paid federal income taxes amounting to less than 10 percent of their total worldwide earnings.

The average effective tax rate for the 168 firms in the survey was 13.04 percent of the companies' total income - just under one-fourth of the 48 percent corporate tax rate prescribed by law.

Vanik noted that all this was entirely legal. That was his point.The companies were able to reduce their taxes by taking advantage of provisions Congress has written into the law, such as the credit allowed for income taxes paid abroad and deductons permitted for past years' losses.

Vanik said the number of companies paying little or not federal taxes was higher in 1976 than in previous years.

In 1975, 11 firms escaped federal income taxes entirely and 27 paid an effective rate of less than 10 percent.

The list of firms that paid no federal income taxes reads like a Who's Who of corporate America. Included are such giants as U.S. Steel Corp., General Dynamics, American Airlines and Chase Manhattan Corp.

Those paying effective tax rates of less than 10 per cent ranged from Exxon, which paid 8 percent on $7.4 billion in earnings, to American Electric Power Co. Inc., which paid 0.1 percent on $337.4 million.

To qualify for a tax rate of 13 percent or lower, an average American family of four would have to earn $20,500 or less. The companies in the Vanik study had combined pretax earnings of more than $38.7 billion.

One of the main ways U.S. companies escape federal income taxes is through the foreign tax credit, which allows them to reduce their U.S. taxes by the amount of taxes they pay abroad.

In other cases, firms were entitled to large deductions for such expenses as higher energy costs or for losses incurred in previous years, which the tax code allows them to apply to future income.

Nevertheless, Vanik said the figures - combined with similar reports from earlier years - show that big corporations are paying less and less in taxes each year while individual taxpayers are paying more.

Vanik contended that President Carter's new tax-cut proposal "could possible result in exempting almost one-third of America's major corporations from federal income taxation" - a claim now being checked by Treasury officials.

"Can America afford this kind of wholesale freeloading?" he asked.

Vanik's overall estimates were not based on corporate tax returns, which are kept confidential, but on data from the companies' annual reports and statements to the Securities and Exchange Commission.

The estimates were prepared for Vanik by accountants on the staff of the congressional Joint Committee on Taxation, the tax-analysis arm of the House Ways and Means Committee, on which Vanik serves, and Senate Finance Committee.

Among the corporations listed as paying no federal income taxes in 1976 were five major steel producers - U.S. Steel, Bethelehem Steel, Armco Steel, National Steel and Republic Steel.

Other firms include LTV Corp., General Dynamics, Singer, Phelps Dodge, Eastern Airlines, the Southern Co., Pacific Gas and Electric, Philadelphia Electric Co, and Chase Manhattan Corp.

The worldwide earnings of U.S. Steel, before taxes, were listed at $518 million, and those of the Southern Co. $385 million. Pacific Gas and Electric earned $291.7 million, all of it in the United States.

Other corporations whose taxes amounted to less than 10 percent of their earnings included the American Telephone & Telegraph Co., which paid an effective tax rate of 9.5 percent on $6.4 billion in earnings.

Also, the Mobil Corp., with an effective tax rate of 4.5 percent on $3.8 billion in worldwide earnings; Gulf Oil Corp., 7 percent on $2.2 billion, and Esmark Corp., 1 percent on $114.8 million.

In making public his study, Vanik pointed out that the 1976 figures represent a deterioration in the corporate tax picture from the five previous years for which he has complied similar figures.

As recently as 1972, for example, the firms Vanik surveyed paid an average effective tax rate of more than 28 percent - just over double this year's figure of 13.04 percent. The rate has been declining steadily.

In part as a result, he said, the proportion of total federal tax revenues gleaned from corporate taxes has shrunk dramatically, to 16 percent now from 23 percent in 1967. Meanwhile, individual taxes have gone up.