One of the basic physical parameters which defines: (1) the capacity of the solid matrix for the incorporation (sorption) of the impurity and (2) the stability of the solid matrix -impurity system, is the ion-ion interaction potential, representing the main term of the cohesive energy. Using this parameter determined in the frame of the pseudopotential theory and pseudoatomic approximation we have investigated the systems HAP-Sr and HAP-UO2. In analysis, the hydroxyapatite (HAP, Ca10(PO4)6(OH)2) was selected as a model solid matrix since insoluble phosphates, phosphate ceramic and apatite-like materials are candidates for the immobilization of radionuclides. The substitution of calcium atoms by different impurities in HAP can be presented by the formula: Ca10-xMx(PO4)6(OH)2, where 0 ≤ x ≤ 10 and M = Sr2+, UO2 2+. It has been shown that (1) Sr can be safely immobilized by HAP, natural apatites and phosphate rocks in the whole range of its concentrations, and (2) that HAP is not an appropriate solid-matrix for immobilization of UO2 2+ because its incorporation in the low concentration results in a decrease of the matrix stability, stimulating formation of the inhomogeneous structure containing isolated clusters of the UO2- apatite solid phase.