A transport/storage cask for a radioactive material has an inner shell, an outer shell and a circular gamma ray shielding layer and a circular neutron shielding layer both of which are placed between the inner shell and the outer shell. The gamma ray shielding layer is formed by aligning a plurality of gamma ray shielding blocks composed of lead in a block shape in the circumferential direction. The entire gamma ray shielding block in the axial direction is covered with a copper tube having a higher elasticity limit than the gamma ray shielding block. In the above transport/storage cask, the gamma ray shielding layer composed of lead or a lead alloy is not easily deformed.