Among the "kingpins" it criticized was CEO James McNerney Jr. of Boeing. It said he got $18.4 million in pay last year while his company received a tax refund of $605 million.
The study also laid into Citigroup for paying CEO Vikram Pandit $14.9 million while the bank received a net $144 million in tax benefits.
Eighteen of the 26 companies received cash back or credits to apply against tax in the future, according to the report.
The study, a 45-page attack on the corporate tax code, said deductions and credits are allowing companies to lavish big pay packages on executives so they can cut their tax bills while Washington gets less money in a time of trillion dollar-plus deficits.
"Our nation's tax code has become a powerful enabler of bloated CEO pay," the study said.
To calculate tax, the study used companies' own math based on accounting rules. Regulators require companies to estimate their tax bill and disclose it in public documents for investors.
The tax filings that the companies make to the government, typically in September, are private and can differ from the estimate.
Another problem is that the study doesn't count tax the company plans to pay but has deferred to future years. The authors argue that deferred tax can be put off indefinitely.
Charles Bickers, a Boeing spokesman, said that the company's federal tax bill, including deferred tax, was $1.3 billion last year, not a net credit, as the think tank's study found.
Boeing did lower its tax, in part by using a popular tax credit encouraging companies to spend more on research and development. Bickers said that helped the company hire 11,000 people in the United States last year.