U.S. companies are making record profits. And more of the money is staying offshore, and lightly taxed.

A Wall Street Journal analysis of 60 big U.S. companies found that, together, they parked a total of $166 billion offshore last year. That shielded more than 40% of their annual profits from U.S. taxes, though it left the money off-limits for paying dividends, buying back shares or making investments in the U.S. The 60 companies were chosen for the analysis because each of them had held at least $5 billion offshore in...