Mechanical and mathematical models of mechanical multidimensional discrete-continuous systems "carriagetrack" in terms of static and impact interaction in a butt roughness zone are proposed. Their interaction is investigated with the example of a four-axle car and a track for four motion phases in the place of isolated butt roughness. Parameters of static and impact interaction of the carriage with a track in a place of butt joint which takes into account operational and constructive factors are defined.