A tamping machine (5) for simultaneously packing ballast under three sleepers (6) of a track (3) comprises inner, central and outer tamping tools (12,13). The pivot axis (17) of the inner tamping tool(12) is positioned lower than the pivot axis (17) of the central tamping tool (13) by a vertical distance (a). With respect to the two pivot axes (17) of the inner and central tamping tools (12, 13),the longitudinal axes (18) of the two tamping picks (19) are positioned off-centre and closer to the pivot axis (17) of the inner tamping tool (12). This means that even sleepers having a relativelysmall bay width can be packed with ballast without any problems.