A drilling machine for drilling fishplate holes in the end of a rail (10) for a railway or railroad track comprises an electric power drill (20) slidably mounted on a column (14) and supporting on its spindle arbor (58) an annular cutter (26). The column (14) is attached to a base (12) which is firmly clamped to the rail (10) by a clamping mechanism (16a). The latter comprises a replaceable former (30) attached to the base (12) and a clamping jaw (18a) on a lever (48). The latter is actuated by a worm mechanism (72, 74). The jaw (18a) is directly opposite the former (30) and in line with the drill spindle arbor (58). The drilling machine is lightweight and does not have any ground support.
