1. Stability of shells in view of geometrical nonlinearity, elastic plastic deformations, orthotropy of materials, constructive nonlinearity.
2. Construction of the theory of connected problems of thermo mechanical and transonic currents.
3. The proof of existence of decisions of the equations of hyper-parabolic type of different dimension.
4. Optimization of problems of the theory of shells at restrictions on hypotheses.
5. Development of methods linearization and down turn of the order in nonlinear problems of the theory of shells and plates.
6. Stability of nonlinear problems of the theory of shells taking place in an excited environment.

Current Scientific interests:

1. Nonlinear dynamics of the deformable solid body.
2. Wavelet analysis in chaotic vibrations of the distributed mechanical systems (deformable solid body).
3. Argumentation of new scenarios of transition of parametrical vibrations in chaotic in the distributed mechanical systems (deformable solid body).
4. Chaotic vibrations of non-uniform structures.
5. Chaotic vibrations of shells in a temperature field and in a supersonic stream.
6. Optimization of the form of thermoelastic bodies.