We consider the problem of diffraction of a short-wave field by a cylindrical body with the boundary that consists of a half plane and a convex-cylindrical surface jointed together along a straight line. The main feature of the problem under consideration is the jump of curvature of the boundary on the line. The problems with the Dirichlet, Neumann, and impedance boundary conditions are considered. The main terms of asymptotic expansion of wave fields for the problems are constructed.