Yury Shestopalov has been active in several scientific fields, such as mathematical methods for electromagnetics, partial differential and integral equations, numerical methods, inverse problems, nonlinear analysis and various applications in electromagnetic field theory connected with wave scattering, diffraction and propagation in linear and nonlinear media, investigations of materials, optics, contact mechanics, solution to large-scale problems with uncertain data, and supercomputer technologies. Among his scientific interests are studies in didactics of applied mathematics.

• Applied mathematics.
• Mathematical methods for electromagnetic field theory.
• Risk analysis and decision-making methods.
• Mathematics education.

Current research is focused on the development of appropriate computational methods applicable to state-of-the-art supercomputers in electrical engineering and large-scale problems with uncertain data, the creation of new materials, the design of modern antenna equipment, etc.