Plane-parallel displacement of conical bodies in an elastoplastic medium on the basis of the hypothesis of locality is simulated. The parameters of the quadratic velocity model of local interaction are determined by solving the one-dimensional problem of the expansion of a spherical cavity. It is shown that the radial and angular velocity dependent on the stress distribution along the cone at oblique impact. We analyze the behavior of the angular velocity of rotation in time at different positions the center of gravity of a sharp cone.