The problems of transient interaction of deformable bodies with surrounding media are of great practical and theoretical importance. When solving the problems of this kind, the main difficulty is in the necessity to integrate jointly the system of equations which describe motion of the body and the system of equations which describe motion of the medium under the boundary conditions predetermined at the unknown (movable) curvilinear interfaces. At that, the position of these interfaces should be determined as part of the solution process. That is why, the known exact solutions in this area of mechanics of continuum have been derived mainly for the cases of idealized rigid bodies. Different aspects of the problems of transient interaction of bodies and structures with continuum (derivation of the efficient mathematical mod- els for the phenomenon, development of the theoretical and experimental methods to be used for study of the transient problems of mechanics, etc.) were considered in the books by S.U. Galiev, A.N. Guz, V.D. Kubenko, V.B. Poruchikov, L.L Slepyan, A.S. Volmir, and Yu.S. Yakovlev. The results presented by these authors make interest when solving a great variety of problems and show a necessity of joint usage of the results obtained in differ- ent areas: aerohydrodynamics, theory of elasticity and plasticity, mechanics of soils, theory of shells and plates, applied and computational mathemat- ics, etc.