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The different approaches were analyzed to investigate the stress-strain state problems of structurally-anisotropic panels made from composite materials. The classification of mathematical models, analytical methods of calculations, numerical methods of calculations, testing results are presented in this review. New mathematical model relations for the stress-strain state investigation of structurally-anisotropic panels made of composite materials are presented. The primary scientific novelty is the further development of the theory of thin-walled elastic ribs related to the contact problem for the skin and the rib with an improved rib model. A promising area of research is the design of composite aircraft structures in the field of production technologies. We consider the residual thermal stresses and the preliminary tension of the reinforcing fibers with respect to the panel production technology. The stress-strain state problem results in the boundary value problem when solving for the eighth order partial derivative equation in the rectangular field. A computer program package is developed in MATLAB. The computer program package has been utilized for multi-criteria optimization of the design of structurally-anisotropic aircraft composite panels. The results of testing series are presented as the verification of the proposed mathematical model.