A theoretical model is proposed for stress relaxation in decahedral core-shell nanoparticles through formation of circular prismatic misfit dislocation loops at the core-shell interface. The critical conditions for stress relaxation are determined and discussed in comparison with those for single-crystalline core-shell nanoparticles. It is shown that decahedral core-shell nanoparticles should be less stable with respect to misfit dislocation generation than single-crystalline ones when the lattice parameter of the core is larger than that of the shell. Theoretical results are compared with experimental observations available in the literature and are shown to be in a good agreement with the latter.