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A concept of phase and chemical correspondence in the system matrix material–host rock is suggested for methods of storing radioactive wastes in crustal rocks. This principle allows directional synthesis of certain mineral matrixes. Matrix materials, which are solid solutions of minerals for immobilization of alkaline, alkaline-earth, rare-earth elements that are radionuclides, were experimentally synthesized. Data are obtained on properties of some mineral solid solutions and on the possibility of graphite processing into stable matrixes. Methods are suggested for the immobilization and separation of noble metals (components of radioactive wastes) and halogens (Br and I). The paper discusses problems in processing minerals of the glass matrixes (borosilicate and aluminophosphate glasses) into stable crystalline matrix materials, and methods are suggested for processing the glass matrixes into mineral-matrix materials.