The invention relates to a flask for transporting and/or storing radioactive substances, in particular spent fuel elements. The flask has a receiving chamber (1) for the radioactive substances and a flask shell (7) surrounding the receiving chamber (1). This shell consists essentially of concrete-like material in the form of a thermally conductive concrete which contains metal particles in pieces, which are for example granular, grainy or in the form of chips, made from a metal having a relatively high coefficient of thermal conductivity, in particular from copper. <IMAGE>