A machine for machining workpieces, including a first column and a second column facing each other according to a first horizontal axis, a guide system guided displacement of at least one of the columns in parallel with the first horizontal axis, one or two tool units, each tool unit being arranged on respective column for controlled displacement perpendicularly to the first horizontal axis, on each column, a workpiece holding device, at least one of the workpiece holding devices being arranged for controlled displacement in parallel with the first horizontal axis, where the workpiece holding devices are arranged for supporting a workpiece between them and for controlled rotation of the workpiece around a workpiece axis parallel with the first horizontal axis.