WASHINGTON — Apple Inc. has used an elaborate web of offshore subsidiaries to avoid paying at least $44 billion in U.S. taxes in the past four years, a Senate investigation has found.

Many of the tactics, such as cost-sharing arrangements, are common among large multinational corporations seeking to shift profits to countries with lower tax rates. The investigation did not find Apple violated any laws.

But three of its subsidiaries in Ireland claim to have no responsibility to pay income taxes to any country, according to a 40-page bipartisan report released Monday by the Senate Permanent Subcommittee on Investigations.

One of those subsidiaries, Apple Operations International, which has no employees but reported $30 billion in income from 2009-2012, has not filed an income tax return in any country for the past five years, the investigation found.

“Apple wasn’t satisfied with shifting its profits to a low-tax, offshore tax haven,” said Sen. Carl Levin, D-Mich., the subcommittee’s chairman and a longtime advocate for tightening U.S. corporate tax laws. “Apple sought the Holy Grail of tax avoidance.”

Chief Executive Timothy Cook is scheduled to testify Tuesday about the company’s tax practices at a hearing by the subcommittee on offshore profit shifting. Apple’s chief financial officer, Peter Oppenheimer, and its head of tax operations, Phillip Bullock, also are scheduled to testify.

In written testimony prepared for the hearing, Apple said the company is “a powerful engine of job creation in the U.S.” and “pays an extraordinary amount in U.S. taxes” — $6 billion last year.

Apple said it does not use “tax gimmicks.”

“Apple has substantial foreign cash because it sells the majority of its products outside the U.S.,” the company said.

The report follows a similar one last year of tax-avoidance practices by Microsoft Corp. and Hewlett-Packard Co. as the subcommittee has focused on multinational high-tech companies, in part because of their ability to shift costs related to intellectual property to low-tax countries such as Ireland, Bermuda and the Cayman Islands.

The findings come as key Republican and Democratic lawmakers, urged on by the White House, are looking to overhaul the tax code, including eliminating some business breaks and lowering the corporate rate to try to make the U.S. more competitive globally.

The U.S. has a 35 percent corporate tax rate and, combined with state and local taxes, has the highest rate among developed nations. The effective rate, however, is much lower.

Companies can stash foreign earnings abroad and do not have to pay U.S. taxes on the money until it is brought back to the U.S. The subcommittee report cited private estimates that U.S. multinational companies have more than $1.7 trillion in foreign earnings parked overseas.

Of Apple’s $145 billion in cash as of April, about $102 billion is overseas. By keeping profits offshore, the company was able to reduce its effective tax rate to 24.2 percent in 2011.

Cook said last week that he planned to urge lawmakers to dramatically simplify corporate tax laws. Among the changes he planned to propose was to lower the rate paid on foreign earnings brought back to the U.S.

Republicans also have pushed for reducing the tax rate on foreign earnings by U.S. firms. But they are at odds with President Obama and many Democrats, who want to set a new minimum tax rate on foreign corporate profits, even if they are never brought back to the U.S.

Ireland is key to Apple’s tax strategy, the investigation found. The country has a 12 percent statutory tax rate, though Apple has negotiated a rate of less than 2 percent on its operations there.

From 2009-2012, Apple shifted $74 billion in income from sales outside of North and South America to Apple Sales International, one of three subsidiaries in Ireland, through complex cost-sharing agreements. For those three years, the company paid less than 1 percent in taxes on those sales, well below even the low rate it had negotiated with Ireland, the report said.

For example, Apple Sales paid $10 million in taxes on $22 billion in earnings in 2011, resulting in a tax rate of 0.05 percent, the report said.

Apple told subcommittee investigators that Apple Sales, along with Apple Operations International and Apple Operations Europe, all based in Ireland, are not responsible for paying taxes there because they are not managed or controlled in that country, a requirement under Irish law. And they are not required to pay taxes in the U.S. because they aren’t physically located here.