The machine is suitable for working wood, materials derived from wood, etc. A rotary cutter (10) is movable past tables (12, 14, 16) for supporting workpieces. The cutter (10) comprises a number of cutting discs set coaxially and separated by spacers. On each table (12, 14, 16) a workpiece can be set at a different level. Movement of the cutter along the ends of the workpieces on a single pass can cut a different joint in each workpiece. The thickness and diameter respectively of the cutting discs determine the width and depth of the slots cut in the workpieces for the formation of joints. The thickness of the spacers determines the spacing of the slots, not only in an individual workpiece but also on a number of workpieces set on the various tables (12, 14, 16).