The problem of stopping of a solid body when it is borne on a round-shaped horizontal plane is studied, assuming that the pressure is distributed according to the law of Bussinesque and the forces of friction are characterized by orthotropic properties. An inference on the location of the instant center of velocities at the moment of stopping is proven. The obtained results may be of practical use in the simulation of the motion of a solid body borne on a round area for solving contact problems and investigating erosive wear.