In the present paper, the wave theory of impact based upon the fact that the wave surfaces of strong discontinuity arise in thin-walled bodies at the moment of impact is suggested. This theory takes into consideration not only flexural waves, but longitudinal waves as well, resulting in extension of a body's middle surface. Besides, an impact process is accompanied by material local deformations, which are taken into account in terms of the Hertz's contact theory. The dynamic deformations behind the wave fronts are determined by means of truncated power series with variable coefficients (what are known as truncated ray series). These two types of deformations are matched on the contact region boundary. A Timoshenko beam and an Uflyand-Mindlin plate are used as the thin-walled bodies, and an elastic sphere or an elastic bar is considered as the striker. The method put forward allows one to obtain analytically all main characteristics of the dynamic contact interaction.
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