Summary: The possibility of using alkali-activated slag-Portland cement for immobilization of dry radioactive waste containing copper ferrocyanide they been confirmed. Because of optimization, the areas of existence of compositions that provide the criterion requirements for strength have been established. Introduction of magnetite additives in the amount of 14...15 wt. % (factor X1), zeolite in the amount of 6.5...7.5 wt. % (factor X2) and dry radioactive waste on the basis of copper ferrocyanide in the amount of 10...12 wt. % (factor X3) provides criterion requirements for compressive strength. The maximum value of strength – 13.2 MPa on the 28th day of hardening is characteristic for the above-mentioned quantities of additives, and it is 1.32 times higher than the standard level of strength. Introduction of zeolite for 6.5...7.5 wt. % allows to reduce the mass and density (1.07 times), radioactivity (1.09 times) of composites. Because of modelling of compound compositions, especially in the expected reactions, the factor X3 shows a weakening factor contributing to the reduction of values of output parameters. Therefore, the introduction of dry radioactive waste into the alkaline slag-Portland cement matrix containing copper ferrocyanide is limited to no more than 12 wt. %. The processes occurring in the volume of the material explain the reduction of mass, density and radioactivity of the compounds. The energy released during radioactive decay of cesium, strontium and other radionuclides is absorbed by magnetite and converted into heat. Heat promotes the removal of physically bound and partially chemically bound water from the structure of tobermorite-like low-basic calcium hydrosilicates, hydrogranates, alkaline-alkaline-earth zeolite-type hydroaluminosilicates, and copper ferrocyanide hydrate shell. However, the passage of radiolysis does not affect the kinetics of strength gain of the compounds, but contributes to the increase of their compressive strength by 1.87 times compared to the strength of the compounds on 7 days of curing