[en] Concrete has been suggested as a possible encapsulation material for long-term storage of low and medium level radioactive waste. At an underground storage of concrete encapsulated waste, a slow release of radioactive elements into the groundwater by diffusion through the concrete must be considered in the safety analysis. The diffusion may be delayed by sorption reactions on the solid. A wide range of long-lived radionuclides may be present in the low and medium level radioactive waste. Here, the sorption and diffusion of iodide and cesium on slag cement paste and concrete has been studied. The influence of four different water phases (pore water, groundwater, Baltic Sea water and sea water) as well as the influence of some added species (carbonate, sulphate and magnesium) has been investigated. A significant sorption of iodide on cement paste in contact with pore water was observed, indicating that the diffusion may be expected to be retarded in this medium. For cesium the highest sorption was found for concrete and groundwater. This means that the sorption increases as the concrete is weathered. Low or insignificant sorption was found for the cement paste, indicating that the ballast is responsible for the Cs-sorption. Carbonatization enhances the Cs-sorption by about a factor of 3. The diffusivity of Cs in concrete and cement paste was determined to between 2x10^-₁₄ and 8x10^-₁₄m₂/s in pore water (where an insignificant sorption was observed). The choice of ballast as well as addition of suitable getters with high sorption of the long-lived radionuclides might decrease the mass transfer rate through the cement. (Authors)