Residual stresses-induced damages in multilayered films grown on technical substrates present a reliability issue for the fabrication and applications of multilayered superconductor systems. Using closed-form solutions for residual stresses in multilayered systems, specific results were calculated for residual stresses induced by the lattice and the thermal mismatches in the system of YBCO/CeO2/YSZ/Y2O3 films on a Ni-5 W substrate. It was concluded that lattice mismatch-induced residual stresses must be relaxed by forming interfacial defects. Studies of residual thermal stresses showed the following. When the thickness of a film is negligible compared to the substrate, the changes of its properties modify the residual stresses in this film layer but have negligible effects on the residual stresses in other layers in the system. On the other hand, when the thickness of certain film layer is not negligible compared to the substrate, residual stresses in each layer can be controlled by adjusting the properties and thickness of this film layer. Finally, the effects of buffer layers on thermal stresses in YBa2Cu3O7-x (YBCO) were addressed by using YBCO/LaMnO3/homo-epi MgO/IBAD MgO/Y2O3/Al2O3 films on Hastelloy substrate as an example.