The construction of a physically nonlinear model of deformation of a rectangular orthotropic plate of average thickness loaded with a transverse uniform distributed load is considered. This model is limited by the scope of small deflections. In the formulation and solution, not only the orthotropy of the plate material was taken into account, but also the nonlinear differential resistance, which was described using the equations of state, constructed using the normalized stress space. The plate fastening is presented in two versions: hinged support and rigid fastening along the contour. An algorithm for solving this class of problems was developed and implemented. A practical solution was made using the MATLAB software package.