A double-wall tank for storing and shipping cryogenic media, which consists of an inner tank that contains the medium, an outer casing spaced some distance from the inner tank, and an evacuated space located between the inner tank and the outer casing, such that at least one permanent magnet is installed in the evacuated space and is arranged opposite a high-temperature superconductor, so that the inner tank is supported in the casing without contact, has the following features: the high-temperature superconductor (8) is located in the evacuated space (5), both the inner tank (1) and the casing (2) have a neck (3, 4), and the necks (3, 4) are arranged concentrically to each other, the neck (3) of the inner tank (1) is a spirally corrugated metal tube (3), whose outer end is attached to the neck (4) of the casing (2).