The subject of this research is the upper load-bearing anisotropic panels of the wingbox of the forward-swept wing of a light aircraft, exposed mainly to longitudinal compression. The panels are fixed along the long sides. The paper considers how to determine the minimum thickness of these panels at a postbuckling state under loads exceeding the operational level. Based on the analytical solution for geometrically nonlinear problems obtained by the Bubnov-Galerkin method, a technique for designing anisotropic panels at a postbuckling state is proposed. To determine the panel’s thickness, the strength criteria for a monolayer of the composite material were used. The main result of the work is a nonlinear equation for the panel’s minimum thickness. It incorporates the equivalence of the membrane stresses due to panel buckling and the limit stresses of the composite package monolayer.