ATHENS/MILAN - January 3, 2012 - Greeks and Italians are taking their money and running, moving it abroad, or even burying it underground for fear the euro zone crisis will topple banks and wipe out what remains of their savings.

Bankers in Greece say worries about the resilience of local banks, coupled with a rise in burglaries, has helped trigger a surge in demand for safe deposit boxes for those who have yet to set up accounts outside the country.

Some are even building their own vaults.

“There has been a big increase in rentals of safe deposit boxes, about fivefold compared with last year,” said one banker at a large, foreign-owned bank. “About 10% of the withdrawals we see are headed there. “The most extreme case was a client who told me he was building a safe under his pool.”

Retail bank deposits in Greece have plunged to five-year lows as fears mount that the stricken nation will fail to meet international lenders’ bailout terms and restructure loans by March, raising the specter of a ditched euro, a return to the drachma, and a sharp devaluation.

With ordinary Greek grandmothers now joining the wealthy in seeking sanctuary from economic chaos, banks have embarked on an interest rate war, with some smaller institutions sweetening terms up to 7% to woo customers.

Bankers said although clients were less panicky than during last September and October, demand remained brisk for foreign currencies such as the Swiss franc, U.S. and Australian dollars, and even Norwegian crowns - or gold.