When a strained film is deposited on a thin substrate or membrane able to relax laterally, the film induces strains into the substrate. Accordingly, the continuing relaxation of the film‐substrate system during deposition generates a nonuniform strain field in the film itself. In this study, the substrate shrinkage or expansion and nonuniform strain distributions within the deposited film are derived. Also, the induced strains due to the pressurization of initially strained and buckled multilayered membranes are analyzed. The lateral expansion of a thin membrane by a compressively strained coating is applied to increase the pressure endurance of the membrane‐coating system. An experimental comparison of pressure endurance is presented for polyimide‐based soft‐x‐ray windows of about a thickness of 200 nm, with thin coatings in various stress states. The strains within the window membrane are calculated by applying the derived formulae successively to the supporting grid and to the membrane cells.