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Composite superconductors like Cu/Nb3Sn and Ag/Bi-oxides are subjected to thermally-induced residual strain by other component materials due to the around 1000 K temperature difference between the high temperatures where the superconductor is formed and the cryogenic temperatures where they are operated. To clarify especially the radial (r) and (θ) tangential strain behaviors, we analyzed elastic-plastically two models, the concentric core model (single-core model) and multi-core model and used two analysis methods, calculation of the force balance equation for the former model and computing of FEM for the former and the latter models. Strains in r and θ directions varied with combination of component materials having large and small thermal expansion coefficients; the superconductor sandwiched by high thermal expansion materials is subjected to larger tensile r-strain and larger compressive θ-strain, as compared with superconducting core only embedded in the matrix. Furthermore it was found that there was a strain distribution by the core location at the inner or the outer. Finally, a better combination of the superconductor with other materials was obtained.