A bridge crane for straightening a rail of a pair of rails along which the crane travels. First and second wheels of the crane are positioned at spaced apart locations along the length of the rail. A radially extending inside flange on the first wheel is positioned facing an inward facing side of the rail at a clearance distance such that the inside flange bears against at least a portion of a plurality of lateral deviations of the rail extending toward the other rail of the pair of rails during travel of the crane along the rails. A radially extending inside flange on the second wheel is provided at a position facing an outward facing side of the rail at a clearance distance such that the inside flange of the second wheel bears against at least a portion of the plurality of lateral deviations of the rail extending away from the other rail of the pair of rails during travel of the crane along the rails. Driving the crane along the pair of rails to cause the inside flange of the first wheel and the outside flange of the second wheel to bear against the respective inward and outward lateral deviations of the rail causes the straightening of the rail. The other rail of the pair of rails is straightened in a similar manner by the flanges of the crane wheels corresponding to the first and second wheels riding on the other rail.