to shield gamma rays each lead block has a cross sectional shape to fit into a corresponding portion located adjacently to the outer surface of the inner shell 1 of the space 8 the lead blocks are inserted into the space 8 along the outer surface of the inner shell 1 the neutron shielding layer 4 is formed of resin blocks each having a thickness required to shield neutrons each resin block has a cross sectional shape to fit into a corresponding portion located adjacently to the inner surface of the outer shell 5 of the space 8 the resin blocks are inserted into the space 8 between the gamma ray shielding layer 3 and the inner surface of the outer shell 5 at the bottom opening of a cylindrical vessel body 9 having the above mentioned structure an inner bottom 10 made of the same material as that of the inner shell 1 is welded to the inner shell 1 and an outer bottom protective bottom 11 is mounted so as to cover the inner bottom 10 at the top opening of the cylindrical vessel body 9 an inner lid 12 made of the same material as that of the inner shell 1 or of stainless steel or the like is mounted and an outer lid protective cover 13 is mounted so as to cover the inner lid 12 in the transport storage cask for a radioactive material having the above mentioned structure gamma rays emitted from a radioactive material contained within the vessel are shielded by the gamma ray shielding layer 3 disposed outside the inner shell 1 thus the inner shell 1 may have a minimum thickness required to function as a pressure vessel thereby improving the efficiency of storage of a radioactive material since.