In an arrangement for laying rail in a railroad track over which railway cars travel, the rails (1) include a lower base flange (1a) and an upper rail head (1b). A molded elastic bearing part (5) is positioned between the lower support member (4) and an upper support plate (3). The elastic part (5) has at least two elements each inclined in the same direction but at different angles to the plane of the track. Extensions of the elements have a common intersection (S) located above the rail flange (1a) on an outer side of the track. As a result, when a load is applied to the track, a circular pivoting motion of the rail takes place about the common intersection (S). Due to the circular pivoting motion the rail head (1d) moves essentially only in the vertical direction, whereby gauge widening does not occur in the rail track when railway cars travel over curved sections of the track.