Riveting apparatus for operation on a workpiece having opposite sides and supported vertically on a horizontal surface comprising a frame having a pair of spaced apart sides movable along the supporting surface and straddling the workpiece, first and second carriages movably mounted on respective sides of the frame and riveting tools on first and second heads on the first and second carriages, respectively, the tools being movable toward and away from the workpiece. The frame travels in a first direction along the supporting surface and along the workpiece, the first and second carriages are movable in a direction substantially perpendicular to the first direction and toward and away from the supporting surface, and the frame is movable in a third direction transverse to the first direction and toward and away from the workpiece. The first and second heads are movable independently about axes substantially parallel to the first direction and to the supporting surface, and both heads are movable independently about axes substantially perpendicular to the first direction and to the supporting surface.The workpiece is supported by a fixture extending along the path of travel of the apparatus and the fixture is supported at spaced locations therealong above the supporting surface by retractable supports separately movable away from the fixture to provide clearance space between the fixture and the supporting surface for travel of a base of the machine.In a riveting system wherein a plurality of such workpieces are supported vertically on a horizontal surface and arranged in spaced apart parallel rows, there is provided a shuttle carriage extending transverse to the workpiece paths and intersecting the paths for receiving the riveting apparatus and transferring it to any of the other workpiece paths in a manner maintaining the same orientation of the apparatus about a vertical axis during the transfer.