Applied investigations of composite aircraft structures show that thin walls or panels of an anisotropic structure are effective in some cases. For thin-walled structures at loads above the operational level, buckling is allowed. Moreover, the task of design based on the post-buckling state becomes much more complicated when it is necessary to take into account the combined loading under biaxial compression and shear. The supercritical behaviour of anisotropic structure's thin panels geometrically nonlinear relations is presented in this paper. For satisfactory description of the panel's supercritical behaviour under hinged support combined loading the form of the deflection function is proposed. The analytical solution based on the Bubnov-Galerkin method how to determine the nonlinear stress-strain state allows obtaining a nonlinear equation connecting the acting flows with the deflection amplitude. Based on the definition of the stress function, equations are written for calculating all components of membrane stresses. Also, expressions are presented for determining bending stresses. It is desirable to take into account when the stress-strain state for geometrically nonlinear behaviour of panels of medium thickness has been determined. The relations of the mechanics for composite panels are presented and, also, the general form of equality for the stresses acting in a monolayer of the composite under combined loading. Further, when using Tsai's criterion for a monolayer, as well for the received nonlinear equations of the stress-strain state with supercritical behaviour, a nonlinear equation was obtained to determine the optimal thickness of the anisotropic panel under its combined loading.