The relevance of the problem is due to the need to improve methods for calculating the dynamic stress-strain state (resonance) of aircraft structural elements made of viscoelastic polymeric composite materials. In recent years, the use of composite viscoelastic materials of structural heterogeneity has had a great impact on the development of the aerospace industry. The complexity of solving such problems is caused by such factors as the essential nonlinearity and structural heterogeneity of the rheological properties of composite materials, as well as by such factors as their interaction with the moving gas. Aerodynamic forces are highly dependent on the position of the structural elements of the aircraft relative to the flow. The magnitude of the aerodynamic force is unknown until the deformation is determined. Also definition of critical states of stability of aircraft structures under the action of gas flow.