<p>The article addresses the problem of determining the optimal geometric parameters for lightweight composite aircraft panels that are reinforced in the longitudinal direction, with the restrictions according to the refined buckling theory. In this context, the thickness of the layers and the dimensions of the elements remain unknown variables. The approach to optimal design focuses on ensuring that the lower critical buckling force exceeds the applied load. A comparison is made between the critical forces governing both the total bending buckling mode and the multi-wave torsional buckling mode. This optimal design dilemma is reduced to a conditional extremum investigation of a multi-variable weight function, utilizing analytical techniques and refined restrictions from buckling theory. The paper also presents innovative mathematical formulations aimed at analyzing the buckling behavior of structurally anisotropic composite panels. The developed model integrates bending with a plane stress state, resulting in a boundary value issue that necessitates solving an eighth-order partial differential equation over a rectangular panel domain. To aid in this research, a software package was created within the MATLAB framework. A comprehensive suite of computer programs was designed to facilitate the optimal design of composite stringer panels used in aircraft. The investigation evaluates how various design parameters influence on the critical buckling forces in both bending and torsional modes. Furthermore, the article details the outcomes of a newly implemented optimal design project focused on the size-weight optimization of carbon-epoxy stringer panels. Adjustments were made to the project by manipulating the layer thicknesses, stringer distances, stringer sizes and angles of the plies in the stacking sequence in accordance with the refined buckling theory applicable to structurally anisotropic composite aircraft panels, leading to the attainment of optimal solutions.</p>