The mathematical model relations for investigation of pre-critical stress-strain state of structurally-anisotropic panels made of composite materials are presented. The pre-critical stressed state of plane angle laminated panels made of polymer fiber composite materials with eccentric longitudinally-lateral stiffening set is considered for further development of refined buckling problems. The new mathematical model for stress-strain state investigation of structurally-anisotropic composite panels is designed. The mathematical model of stiffening rib being torsioned under one-side contact with the skin is refined. Further development of the theory of thin-walled elastic robs related to the contact problem for the skin and the rib with improved rib model reflects the scientific novelty of the research. One takes into account the influence of panel production technology: residual thermal stresses and reinforcing fibers preliminary tension. The resolved equation of eight order differential operator and natural boundary conditions are obtained with variation Lagrange procedure. The schematization of the panel as structurally anisotropic one has been proposed as a design model. Exact analytical solutions for edge problems are considered accordingly general treatment of physical boundary conditions for structure components. The solution in closed form is designed by unitary trigonometric series for the particular case of conformable boundary conditions on two opposite sides. All possible combinations for lateral edges boundary restrictions are examined when bending is integral with plane stress state problem. Computer program package is developed using operating MATLAB environment. The influence of the structure parameters on the inner force factors distribution by the length of carbon-plastic panels has analyzed while longitudinal compression.