UniCredit , Societe Generale and Deutsche Bank may have passed the recent health check of Europe's banks, but they are likely to be among the first big lenders in need of cash if the euro zone crisis worsens.

Europe's stress test of its lenders was widely derided as too soft, but it shone a light on potential trouble spots.

UniCredit could need up to 5.6 billion euros and both SocGen and Deutsche Bank would need about 3 billion euros to reach new global capital standards in the event of a two-year recession and after applying more realistic losses on their euro zone bonds, according to Reuters estimates.

UniCredit is expected to raise capital when the rules become clearer later this year and analysts reckon it could be looking for 5-7 billion euros. Whether more big banks join it is likely to hinge on the speed and severity with which the euro zone crisis plays out.

Many banks out there will have to raise capital in the event there's contagion due to the Greek, Portuguese and Irish issues, said Guy de Blonay, who runs Jupiter's Financial Opportunities Fund.

A rescue deal for Greece last week eased fears the crisis will spread. But the threat remains real, and some think that because the first selective default has occurred it is now more likely Ireland and Portugal will follow.

That would see pressure build quickly on banks to stockpile capital in the face of losses in troubled economies, with politicians keen to show the financial sector playing its part.

However the banks will wish to delay any cash-raising operations.

Investors are currently giving the sector a wide berth because of its risk profile. Europe's bank shares hit a two-year low last week and most are trading below book value, so any fundraising would be painfully dilutive for shareholders and unlikely to attract huge numbers of subscribers.

Despite their difficult trading conditions, most banks are still in denial about the extent of capital needed to restore confidence, industry observers say.

The European Banking Authority's (EBA) stress test showed core capital at UniCredit and SocGen would fall to 6.6 percent under a two-year recession and at Deutsche Bank it would drop to 6.5 percent.

That was above the minimum level of 5 percent, but below the 7.7 percent average of the 90 banks tested. In addition, critics point out that the pass mark was not high enough and the test failed to impose realistic haircuts on holdings of sovereign debt and thus accurately portray the banks' resilience to any future economic shocks.

JPMorgan analysts used EBA test data to run their own stricter tests, including applying sovereign losses, and concluded an estimated 20 European banks need to raise 80 billion euros. Morgan Stanley said Europe's banks needed 40 billion euros and Credit Suisse estimated 83 billion euro of extra capital would be needed across 49 banks.

Brussels unveiled tougher capital laws last week that could force banks in Europe to raise a total of 460 billion euros to better shield taxpayers in a financial crisis. The banks have plenty of time to reach the 7 percent core capital standard, but laggards are likely to be punished by investors.

Twenty-eight of the world's biggest banks have also been told they need to hold extra capital due to their importance and the threat they would pose to economic stability should they hit trouble. Deutsche Bank, SocGen and UniCredit are all expected to be on the list, probably needing 1-2 percent extra capital.

Pressure on the banks could mount even further when Mario Draghi becomes ECB chairman in November. Draghi drove top Italian banks -- bar UniCredit -- to raise a collective 11 billion euros earlier this year, an impressive amount when set against a total of 50 billion euro raised by Europe's banks in 2011.

CAPITAL NEEDS

Deutsche, SocGen, Unicredit and Royal Bank of Scotland ranked in the third quartile in terms of capital strength under the EBA's test, making them the most vulnerable of the big banks.

Several more are likely to join UniCredit in raising cash -- even if they could instead rebuild capital through retained earnings and asset sales -- as a public act of reassurance to the markets, a senior investment banker said.

Such a move would allow them to tell investors: Stop focusing on my capital level and start focusing on my business again, the banker said.

Deutsche Bank has no plans to raise capital after raising 10 billion euros last year to fund its Postbank deal, sources have told Reuters. It is confident it can meet any shortfall through earnings and reducing its risk weighted assets (RWAs).

Deutsche would need an extra 2.5 billion euros to lift core capital to 7 percent under the EBA's test, and would lose around 1 billion euros if current market prices on its Greek and other peripheral euro zone bonds were applied, according to Reuters estimates.

SocGen meanwhile would lose 1-1.5 billion euros if haircuts close to current market prices were applied to its Greek, Italian and other peripheral euro zone sovereign debt and would need 1.8 billion to get to a 7 percent core capital.

UniCredit could need between 2 billion and 4 billion euros if the same haircuts were taken into account, mainly due to its holding of 47 billion euros of Italian bonds, and another 1.6 billion to reach 7 percent.

Banks and analysts have warned of flaws in the EBA's methodology, and pointed out that investment bank business was dealt with more harshly than retail banks.

Banks had to use static balance sheets when they participated in the stress test exercise, meaning ongoing action to reduce assets could not be included. Securitizations and trading income were also harshly dealt with.

An example: the outcome for RBS was skewed because the bank had to use historical trading income figures which incorporated its huge 2008 loss. It also failed to benefit from the substantial shrinking of its assets.

SocGen said strong first quarter profits, paying dividends in shares and deleveraging its balance sheet hadn't been included in the EBA's test.

Deutsche Bank said the test did not take account of its plan to reduce risk weighted assets and UniCredit said it did not take into account the effect of convertible bonds to boost its capital.

(Additional reporting by Ian Simpson in Milan, Philipp Halstrick in Frankfurt; editing by Sophie Walker)