The content of binding agent components and aggregates of shielding concrete (portland cement, gabbro, silicate, granite, hematite, magnetite, limestone) has been studied to identify nuclides contributing to the long-lived radioactivity of concretes used in nuclear reactor shielding. Elemental content was determined by neutron activation analysis at the IBR-2 reactor of the Laboratory of Neutron Physics (JINR). It is shown that the nuclides mainly responsible for the long-lived activity are152Eu,154Eu,60Co and134Cs. Based upon the experimental data obtained, calculations of the specific activity of concrete ingredients being irradiated for 30 years by a unit neutron flux density have been performed, and diagrams of the dependence of the specific activity versus time are presented. It is recommended that the application of such media as magnetite, serpentinite, chromite to shielding structures should be abandoned. Estimations of the dose rate from concrete structures containing various aggregates for the limiting case of semi-infinite space are given. The results obtained can form the basis for the optimal choice of the materials when constructing the concrete shielding of neutron sources.