The Federal Reserve's most recent stress test shows 29 out of 30 U.S. banks met their stress test capital requirements. Only one smaller bank, Zions Bancorporation, failed to pass the annual test. Shares of that Salt Lake City-based bank's stock fell more than 1 percent in extended trading.
The results showed continued improvement in banks' financial positions since the 2008 crisis, the Fed said. That built on positive results in last year's tests.
The Fed will announce next week whether it will approve plans by some of the banks to increase dividends or buy their own stock.
Following the announcement, Discover Financial, one of the 30 banks tested, said it will increase its quarterly dividend by 4 cents to 24 cents per share.
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The annual testing has become an increasingly important tool for regulators to ensure that banks are not eating too much into their capital cushions, by examining how banks would weather a hypothetical major market shock.
Earlier, analysts predicted that the larger U.S. banks would most likely meet the Fed's requirements, having reduced their leverage, the amount of debt compared to shareholder equity, since the 2007-2009 financial crisis.
(Read more: New round of bank stress tests: What to watch for)
Bigger fireworks could come next week, when the Fed will either approve or reject each firm's plans to pay dividends to shareholders or buy back shares.
The Fed conducts stress tests each year to measure how banks' loan books and security portfolios would hold up under extreme economic scenarios not unlike those experienced during the last crisis.
Some 30 banks participated in this set of tests, up from 18 last year.
—CNBC and The Associated Press contributed to this article.