The investigation is expected to set up a potentially explosive confrontation between a bipartisan group of lawmakers and Timothy D. Cook, Apple’s chief executive, at a public hearing on Tuesday.

Congressional investigators found that some of Apple’s subsidiaries had no employees and were largely run by top officials from the company’s headquarters in Cupertino, Calif. But by officially locating them in places like Ireland, Apple was able to, in effect, make them stateless — exempt from taxes, record-keeping laws and the need for the subsidiaries to even file tax returns anywhere in the world.

“Apple wasn’t satisfied with shifting its profits to a low-tax offshore tax haven,” said Senator Carl Levin, a Michigan Democrat who is chairman of the Senate Permanent Subcommittee on Investigations that is holding the public hearing Tuesday into Apple’s use of tax havens. “Apple successfully sought the holy grail of tax avoidance. It has created offshore entities holding tens of billions of dollars while claiming to be tax resident nowhere.”

Thanks to what lawmakers called “gimmicks” and “schemes,” Apple was able to largely sidestep taxes on tens of billions of dollars it earned outside the United States in recent years. Last year, international operations accounted for 61 percent of Apple’s total revenue.

Investigators have not accused Apple of breaking any laws and the company is hardly the only American multinational to face scrutiny for using complex corporate structures and tax havens to sidestep taxes. In recent months, revelations from European authorities about the tax avoidance strategies used by Google, Starbucks and Amazon have all stirred public anger and spurred several European governments, as well as the Organization for Economic Cooperation and Development, a Paris-based research organization for the world’s richest countries, to discuss measures to close the loopholes.

Still, the findings about Apple were remarkable both for the enormous amount of money involved and the audaciousness of the company’s assertion that its subsidiaries are beyond the reach of any taxing authority.

“There is a technical term economists like to use for behavior like this,” said Edward Kleinbard, a law professor at the University of Southern California in Los Angeles and a former staff director at the Congressional Joint Committee on Taxation. “Unbelievable chutzpah.”

While Apple’s strategy is unusual in its scope and effectiveness, it underscores how riddled with loopholes the American corporate tax code has become, critics say. At the same time, it shows how difficult it will be for Washington to overhaul the tax system.