Abstract: A track tamping machine has a machine frame extending in a longitudinal direction and tamping units mounted to the machine frame. A first or upper transverse guide extends in a transverse direction perpendicularly to the longitudinal direction. Two sliding blocks are mounted for displacement in the transverse direction independently of one another on the upper transverse guide. A second or lower transverse guide is positioned vertically below the upper transverse guide and parallel thereto. The lower transverse guide is mounted in the sliding blocks for displacement relative thereto in the transverse direction. Two inner unit frames are connected to a respective one of the sliding blocks and support a tamping unit in each case. Two outer unit frames are positioned in each case farther from a vertical machine center line—with regard to the transverse direction—than an adjacent one of the inner unit frames and support a respective tamping unit.