Mathematical theory of elasticity; Theory of anisotropic plates and shells; Theories of plasticity, creep and viscoelasticity: Magnetoelasticity; Contact and mixed boundary-value problems of deformable solids mechanics; Interaction of thin-shelled systems with different physical fields and media; waves propagation in continuous media; Composite materials and design optimization of constructions; Mechanics of soils, basis and foundations; Mechanics of seismic center and seismic waves propagation in layered media; Mechanics of fluids and mixtures; Mechanics of robotic systems and optimal control.

The creep theory of homogeneous and nonhomogeneous aging materials is built; The classical, asymptotic and improved theories of layered anisotropic plates and shells is built; The magnetoelasticity theory of thin-shelled bodies is built; An invention is carried out on low-stress phenomenon (1978); Over 20 monographs are published, most of which is translated into different languages.

Institute has participated in the All-Union Symposiums on theoretical and applied mechanics, International Congresses on solid mechanics and numerous conferences. Organized the All-Union Symposiums on theory of plates and shells, theory of elasticity, problems of dynamic of interactions. Joint scientific investigations are carried out together with: Berkeley University of California (USA), Pierre and Mary Curie University of Paris (France) and University of Pavia (Italy). The employee of the Institute have been awarded: SOROS International Foundations two grants, two grants of INTAS program, as well as a three grants of DAAD program, as well as a prize of Japanese organization SICE.