The Federal Reserve said Monday that it will release its findings this week on how the country’s biggest banks would fare under a nightmare economic scenario.

The latest round of stress tests examine whether the banks could withstand a crisis in which unemployment hits 13 percent, stocks fall by half, and housing prices drop 21 percent. Banks that are deemed healthy enough would be allowed by regulators to raise dividends for shareholders or buy back shares — both of which can boost their stock prices. Those that don’t pass the test would have to raise their capital levels and face serious questions from shareholders. The results will be out Thursday afternoon.

More than three years after the financial meltdown, the Fed is under pressure to prove it can monitor the banks and prevent a repeat crisis. At the same time, bank executives such as Jamie Dimon of J.P. Morgan Chase are agitating for the Fed to loosen capital requirements on healthy banks so they can return more capital to investors.

Compared with past stress tests, said former Federal Deposit Insurance Corp. chairman Sheila C. Bair, “the process is evolving and it’s getting better. . . . The stress scenarios are much more severe than they have been in years past.”

The Fed is scrutinizing the country’s 19 biggest banks, a list that includes Bank of America, Citigroup, Goldman Sachs and Wells Fargo. The central bank plans to release unprecedented levels of detail about how the banks would fare in a crisis, including their earnings and loan losses.

A year ago, the Fed ran another series of tests on large banks and allowed most of them to increase returns to shareholders by billions of dollars.

Repurchases of stocks jumped from $477.5 million in the first quarter of 2011 to $5.33 billion in the second quarter, according to SNL Financial. In addition, 123 U.S. banks and thrifts either raised or began offering dividends, compared with 78 in 2010 and 39 in 2009.

Critics worry that allowing banks — especially those that are still too big to fail — to spend money on dividends and buybacks means they will have less capital on hand in case of another economic crisis. The result, they fear, would be another bailout funded by taxpayers.

“If they’re not willing to break up the banks, [regulators] need to do as much as possible to reduce the impact of the next crisis on the taxpayer,” said Neil Barofsky, former special inspector general for the Troubled Assets Relief Program, or TARP. “The most obvious tool they have available to them is by forcing high levels of capital.”

The banking industry is still facing some challenges left over from the housing bust. There are legal liabilities related to foreclosure fraud. The recovery of the U.S. economy remains tepid. In addition, unresolved sovereign debt issues in Europe still loom large.

Analysts expect the Fed to let most banks go ahead with their plans to raise dividends or buy back shares. But banks are having trouble finding new sources of revenue.

“I think you’re probably going to see people say, ‘Hey, the banks are fine, the banks are okay,’” said Matt McCormick, portfolio manager at Bahl & Gaynor Investment Counsel in Cincinnati. “Their fundamentals are better, but they’re still questionable. They’ve had negative revenue growth year over year, quarter over quarter.”

For instance, Goldman Sachs reported net revenues of $28.8 billion for 2011, down 26 percent from 2010.

Others point out, however, that banks are boasting much healthier balance sheets than before, and say it’s time for the government to allow them more leeway.

“Bank capital levels are so vastly stronger than they were going into the crisis. It’s no comparison,” said Chris Kotowski, managing director and senior analyst covering large banks at Oppenheimer & Co.

The 19 bank holding companies have raised their Tier 1 common capital levels, a core measure of a bank’s ability to withstand stress, to $759 billion in the fourth quarter of 2011, compared with $420 billion in the first quarter of 2009, according to the Federal Reserve.