NEW YORK (Reuters) - Regulators are ordering some of the largest US banks to get tens of billions of dollars of capital to cushion themselves in the event of a deep economic downturn.

While the capital shortfalls at the 19 largest US banks are much larger than analysts had expected, bank shares soared, extending a two-month rally as investors got more clarity over how well the industry will cope with perhaps the most severe recession since World War II.

Among banks needing capital, Bank of America Corp shares closed up 17.1 percent, Citigroup Inc rose 16.6 percent and Wells Fargo & Co rose 15.6 percent. The Standard & Poor's Financials Index gained 8.1 percent.

"The market likes the certainty of putting numbers on the worst-case scenarios of how much capital these banks need," said Chris Armbruster, an analyst at Al Frank Asset Management, Laguna Beach, California.

After conducting "stress tests" of the 19 biggest banks, the government has told Bank of America it needs $34 billion of capital, roughly triple what had been expected, an industry source familiar with the results said.

Citigroup needs $5 billion, reflecting its previously announced plan to convert some preferred shares into common stock, a person familiar with the matter said. GMAC LLC , the auto and mortgage lender, needs $11.5 billion, a person familiar with that matter said. Wells Fargo needs $15 billion, Bloomberg News said, while Regions Financial Corp needs some capital, the Wall Street Journal said.

Bank of New York Mellon Corp does not need capital, a person familiar with the matter said. American Express Co , Goldman Sachs Group Inc, JPMorgan Chase & Co , MetLife Inc and Morgan Stanley also do not need capital, according to published reports.

Banks may cover any capital shortfalls through a mixture of asset sales, share sales, and perhaps the conversion of the preferred shares into common stock.

All the companies declined to comment. The various sources were not authorised to speak because the official stress test results are not public.

The tests are a key element of the Obama administration plan to stabilise lenders, and about 10 of the 19 banks are expected to need capital.

Final results are due late today, and the White House will await them before commenting on potential management changes at banks, spokesman Robert Gibbs said.

The government has spent three months conducting stress tests to determine banks' capital needs should economic conditions worsen more than many economists now expect.

If banks were required to raise more capital than expected, it might unnerve investors who had hoped the stress tests might show the industry was in less dire condition than feared.

An inability to sell enough assets could require some banks to convert earlier government aid into common stock, making the government one of their biggest shareholders.

Citigroup analyst Keith Horowitz wrote that banks, other than his own, may need to raise $75 billion after the tests.

Analysts believe other banks that may need capital include Fifth Third Bancorp, KeyCorp, PNC Financial Services Group Inc and SunTrust Banks Inc.

Federal Deposit Insurance Corp Chairman Sheila Bair said the results should be "confidence instilling."

Bank of America's stress test results are certain to increase pressure on chief executive Kenneth Lewis, who was ousted as chairman last week in a shareholder vote.

That ouster could also lay the groundwork for his departure from his employer of 40 years, including the last eight as CEO. The largest US bank has already received $45 billion of government help.

"We know what Bank of America's problem is now, but we don't know what the solution is," said Ben Wallace, an analyst at Grimes & Co in Westborough, Massachusetts.

Lewis told analysts on an April 20 conference call that "we absolutely don't think we need additional capital", but added: "Make no doubt about it, credit is bad, and we believe credit is going to get worse."

Critics fault Lewis for failing in December to back away from the Merrill merger or disclose Merrill's sinking finances, as well as for Bank of America's role in the $3.6 billion of bonuses that Merrill paid out.

The bank might raise capital by converting into common stock some of its $30 billion of privately held preferred shares, or by selling its stakes in China Construction Bank Corp and Brazil's Itau Unibanco.