Aircraft composite structure design in the field of production technology is the outlook research trend. New mathematical model relations for the buckling investigation of structurally-anisotropic panels comprising 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. One considers the residual thermal stresses and the preliminary tension of the reinforcing fibers with respect to panel production technology. The buckling problem results in the boundary value problem when solving for the eighth order partial derivative equation in the rectangular field. The solution is designed by a double trigonometric series and by a unitary trigonometric series. The results of testing series are presented.

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