The article presents the results of computational studies of the radiation changes in serpentinite concretes of "dry" radiation shield of the Water-Water Energetic Reactor (WWER/VVER) type of nuclear power plants built in the Russian Federation and other countries. The research was carried out in connection with the increase in radiation loads on the concrete of the "dry" protection of modern nuclear power plants, and also in connection with the possible use in "dry" protection of the modern nuclear power plants of concretes with serpentinite aggregates which mineral composition and structure differ from the composition and structure of the previously used serpentinites. The calculation studies were performed using the developed and experimentally tested methods for the analytical determination of radiation and thermal changes in concretes and their components. It was found out that the relative number of displaced by irradiation atoms from 0.026 to 0.1, degree of perfection of the crystal structure of serpentinite minerals, availability of impurities in serpentinite minerals (magnetite, chlorite, olivine, pyroxenes, hornblende, brucite, magnesite, calcite, dolomite, ankerit, mica, feldspar in quantity from 0 to 40%, medium mineral grain size in the range of 0.0001 cm up to 0.02 cm influence on the radiation changes in the volume and strength of serpentinite concretes. There was also performed comparison of radiation and thermal changes. The research has showed that the lowest radiation changes will occur in the serpentinite concrete with aggregates consisting only of serpentine, especially with imperfect structure. The availability and quantity of magnetite, chlorite, calcite, brucite, feldspars and mica show insignificant influence on the radiation changes. The presence of dolomite, magnesite, ankerite and especially olivine, hornblende, pyroxenes with an increase in their volume content, as well as growth in the size of grains of minerals, the radiation changes in serpentinite concretes may grow up to 2-4 times. By increasing the duration of exploitation and power capacity of the reactor, as well as by extending the service life of a nuclear power plant, the radiation changes in the serpentinite concretes of "dry" radiation shield may grow up to 6-12 times.