Method for long-term dry storage of spent nuclear fuel includes injecting the inert gas into a cavity formed in a cask between inner and outer lids under pressure greater than the pressure of the inert gas in the inner cavity of the cask in which the spent nuclear fuel is located. The cask contains a body with a spent nuclear fuel container placed in it, tight inner and outer lids forming a cavity into which the inert gas is pumped under pressure greater than the pressure in the inner cavity of the cask. The outer lid comprises a labyrinth hole closed with a flange and sealed with a gasket. The flange comprises an angle valve, to which at least two pressure sensors are connected. The angle valve and sensors are covered with a protective cover during long-term storage. The gasket is installed in an annular groove of the lower flange.