Abstract: A ballast tamping machine comprises a machine frame supported on a track by undercarriages for moving in an operating direction, a track lifting and lining unit mounted on the machine frame and operable to correct the track position, a reference system controlling lifting and lining of the track by the track lifting and lining unit, and two adjoining tamping heads arranged sequentially on the machine frame in the longitudinal direction at a respective track rail. Each tamping head comprises ballast tamping tools reciprocable towards each other in the longitudinal direction at the gage side and the field side of the rail, drives for vertically adjusting the ballast tamping tools of each tamping head independently of the vertical adjustment of the ballast tamping tools of the other tamping head for immersing tamping picks on the ballast tamping tools in the ballast underneath the track.