Abstract <p>The equations of the mathematical model for analyzing the static strength of layer-anisotropic composite panels of aircraft with medium-to-thick skins, considering the transverse shear deformations, are provided. An approach to solving the static strength problems within the framework of a new tenth-order partial differential governing equation is developed. For the special case of compatible boundary conditions on the longitudinal sides of the panel, the integral of the equation is represented analytically using the single trigonometric Fourier series. New analytical constraints on the objective function for optimal design of aircraft layer-anisotropic medium-to-thick composite skins are constructed according to the refined theory. The results of determining the layer-by-layer stress-strain state of a thick orthotropic skin at the center of the panel in the coordinate system associated with the layer are presented for flat rectangular carbon fiber skins compressed in the longitudinal direction. The feasibility of using the mathematical models reduced to the analytical solution of static strength problems for the governing equation with a tenth-order linear differential operator as constraints in the design of structurally anisotropic composite panels for advanced aerospace applications is substantiated. </p>