Internal residual stresses significantly influence the overall mechanical properties of multi-layer systems and consequently affect the coated material＇s performance. The determination of residual stresses within coatings has been extensively carried out for thin (the coating thickness being less than the substrate thickness) films (Stoney, Roll, etc.) and for thick (the coating thickness being approximately equal to the substrate thickness) films (Timoshenko, Inoue, etc.). This work extends currently existing models to cover cases where the coating thickness approaches that of the sheet substrate. We developed relationships for the determination of the first-order residual stress. The construction of these models was carried out using a one-dimensional analysis based on beam theory (the width-to-thickness ratio of the system being less than 5). As suggested by Timoshenko and later on by Hoffman, we also introduced the bi-axial modulus for isotropic stresses when the thin plate theory (the width-to-thickness ratio of the system being greater than 5) is used. Under forces and moments resulting from coating initial residual stresses, we consider that the bi-layer material exhibits a radius of curvature, R. The final equilibrium state is obtained by the simple and pure bending of the bi-layer material. From the two equilibrium conditions (force and moment), the model for the initial residual stress is derived as a function of mechanical (Young＇s modulus and Poisson＇s ratio of the substrate and of the coating) and geometrical (thickness of the substrate and of the coating) characteristics of the bi-layered system. This model derived for initial residual stresses ignores the in-plane deformation of the bi-layer material and can be applied to compliant coating materials deposited onto stiff substrates or to thin coating layers deposited onto thick substrates. Furthermore, in order to consider the in-plane deformation which implies that the strain in the coating causes a strain in the substrate (as opposed to the above situation where the substrate imposes the strain in the coating one-sidedly), this model was rewritten by introducing the stiffness ratio. The relationship obtained (for the in-plane deformation) is equivalent to that of Inoue and it is, of course, the most applicable since it can be applied to thin and thick coating layers of compliant or stiff materials deposited onto compliant or stiff substrates.