Abstract: A tangential grinding machine slidable on rails to be ground includes a base structure mounted on wheels slidable on the rails to be ground; a grinding unit freely slidable along the cross-members of the base structure, the grinding unit having a frame rigidly movable vertically relative to the base structure towards and away from the rail, the frame being rigidly coupled to at least two longitudinally aligned plates supporting a grinding wheel with a rotatable axis transverse to the rail longitudinal axis; and a bar hinged at its ends to the base structure and to the grinding unit respectively, there being connected to the frame supporting the plates a gear motor provided with a vertical axis worm gear, the end of which rests on the grinding unit, a control unit being associated with the gear motor to control frame descent following wear of the grinding wheel.