The sorption parameters of a number of natural materials, diatomite, tripoli, and bentonite rock, were studied in relation to the Cs-137, Sr-90, and U-233 radionuclides. It was shown that the efficiency of Cs-137 and Sr-90 sorption is directly proportional to the content of the clay component (illite and smectite minerals) in the sample and to the cation-exchange capacity (CEC), which indicates the ion exchange sorption mechanism of these radionuclides. The sorption parameters of the studied samples with respect to Cs-137 and Sr-90 decrease in the series bentonite rock > diatomite > tripoli. The Cs-137 distribution coefficients (K-d) of bentonite rock and diatomite samples in the NaNO3 concentration range of 0.1-1.0 mol/dm(3) are more than 10(3) cm(3)/g, which evidences high sorption-selective parameters of these rocks with respect to Cs-137. The K-d values of Sr-90 on all the studied sorbents upon sorption from tap water are 1-2 orders of magnitude lower than the sorption of Cs-137, which is caused by the competitive sorption of calcium ions. The main mechanism of U-233 sorption is physical adsorption on the surface of minerals, which is proportional to the specific surface area of minerals. The K-d values of U-233 for all studied sorbents are relatively low and are in the range of 48-160 cm(3)/g. It was shown that natural sorbents, bentonite clays and diatomites, can be used as effective geochemical barriers to prevent the migration of cesium and strontium radionuclides from radioactive waste storages.