<p>The defining equations of the simplified theory of physically nonlinear deformation of a structurally orthotropic body were obtained in an explicit form, based on the provisions of O. A. Ilyushin’s theory of small elastic-plastic deformations for an isotropic body and B. E. Pobedrya’s tensor-quasilinear theory of plasticity of an anisotropic body, when under compression or tension in the direction of one of the axes of orthotropy, plastic deformations do not occur. The equation was also modified for the case when the orthotropy axes do not coincide with the coordinate axes in one of the orthotropy planes. Simple establishing experiments for samples of orthotropic material for the determination of four nonlinear functions of the given equations were described. These equations can be used to build calculation theories in a physically nonlinear setting of structural elements made of orthotropic materials, which are reduced to two-dimensional calculation models. A physically nonlinear calculation of a bending three-layer plate in a refined formulation was performed taking into account transverse shear and transverse compression deformations. Maximum deflections were determined, as well as yield zones at different loading levels and the failure region in the bearing layer of the plate.</p>