Non-linear problems of vertical immersion of cylindrical and spherical shells into a thin layer of fluid as well as a problem of oblique impact of a hollow rigid body on a thin layer of fluid were investigated. In all problems the fluid was considered as an ideal incompressible liquid, with potential motion only. For analysis of hydro-dynamic component of the problems the method of matched asymptotic expansions was used. For the solution of the elastic component of the problems the normal-mode method was applied. In the problem of oblique impact of a hollow rigid body on a thin layer of fluid the location of the separation point of the free fluid boundary from the smooth surface of the moving body was determined.
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