A composition for use as a radiation shield. The shield is a concrete product containing a stable uranium aggregate for attenuating gamma rays and a neutron absorbing component, the uranium aggregate and neutron absorbing component being present in the concrete product in sufficient amounts to provide a concrete having a density between about 4 and about 15 grams/cm.sup.3 and which will at a predetermined thickness, attenuate gamma rays and absorb neutrons from a radioactive material of projected gamma ray and neutron emissions over a determined time period. The composition is preferably in the form of a container for storing radioactive materials that emit gamma rays and neutrons. The concrete container preferably comprises a metal liner and/or a metal outer shell. The resulting radiation shielding container has the potential of being structurally sound, stable over a long period of time, and, if desired, readily mobile.