The Japanese are hoarding over $300 billion under their mattresses and that cash will likely stay there unless a crisis of epic proportions sparks capital flight, analyst say.

"The money has been sitting there so long, it's difficult to pin down what will prompt people to spend the cash," Mizuho Securities' chief market economist Yasunori Ueno told CNBC by phone.

The notion came to public attention last year when Finance Minister Taro Aso scolded the Japanese for sitting on 880 trillion yen ($7.33 trillion) in cash, which was widely reported by the local press as being 'kept under mattresses'.

"It's ridiculous – the money should be deposited at financial institutions so the banks can fund promising industries," said Aso, according to a Sankei newspaper report.

But that figure was based on household cash deposits at Japanese banks, rather than hidden under mattresses, Ueno said. As per his calculations in a note dated March 25, households are probably hoarding around 36 trillion yen ($301 billion) of cash.

"It's like an iceberg – it just won't melt," said Dai-ichi Life Research Institute (DLRI) chief economist Hideo Kumano. "It will just sit there, immobile and frozen in time."

Cash is king

In many countries hoarding cash at home is synonymous with the underground economy, but the reasons in Japan are more mundane.

"Under deflation, cash is king," said DLRI's Kumano, although he added that an unknown portion of the cash is probably just being hidden from the taxman.