Yu.V. Tokovyi investigates fundamental and applied problems of thermomechanics of structurally heterogeneous and thermosensitive (in particular, functionally graded) bodies, direct and inverse problems of the mechanics of deformable solid bodies, and also develops advanced analytical-numerical methods of mathematical physics. With his direct involvement, effective mathematical models and methods for analyzing the stress-strain state of bodies with internal and surface structural defects under the influence of fields of various physical nature have been developed. The proposed methods for studying thermal and residual stresses in thick-walled heterogeneous pipeline elements, which significantly enhance the reliability, stability, and durability of modern engineering objects, have considerable practical significance.