A machine for machining workpieces, comprising: a first column and a second column, the first column and the second column being arranged facing each other according to a first horizontal axis; a guide system for guided displacement (Z1, Z2) of at least one of the first column and the second column in parallel with the first horizontal axis; a first tool unit (11; 11A) adapted for supporting and driving a first rotatable tool (12; 12A), the first tool unit (11; 11A) being arranged on the first column for controlled displacement (X1; Y1) in relation to the first column in parallel with a second axis (X; Y) perpendicular to the first horizontal axis; a first workpiece holding device arranged on the first column, the first workpiece holding device being arranged for controlled displacement in relation to the first column in parallel with the first horizontal axis; a second workpiece holding device arranged on the second column; wherein the first workpiece holding device and the second workpiece holding device are arranged for supporting a workpiece between them and for controlled rotation (C1, C2) of the workpiece around a workpiece axis parallel with the first horizontal axis; and wherein the machine comprises a drive system (32, 33, 18) for: - controlled positioning of the first column in relation to the second column, in parallel with the first horizontal axis, and - controlled positioning of the first workpiece holding device in relation to the first column, in parallel with the first horizontal axis. a first column and a second column, the first column and the second column being arranged facing each other according to a first horizontal axis; a guide system for guided displacement (Z1, Z2) of at least one of the first column and the second column in parallel with the first horizontal axis; a first tool unit (11; 11A) adapted for supporting and driving a first rotatable tool (12; 12A), the first tool unit (11; 11A) being arranged on the first column for controlled displacement (X1; Y1) in relation to the first column in parallel with a second axis (X; Y) perpendicular to the first horizontal axis; a first workpiece holding device arranged on the first column, the first workpiece holding device being arranged for controlled displacement in relation to the first column in parallel with the first horizontal axis; a second workpiece holding device arranged on the second column; wherein the first workpiece holding device and the second workpiece holding device are arranged for supporting a workpiece between them and for controlled rotation (C1, C2) of the workpiece around a workpiece axis parallel with the first horizontal axis; and wherein the machine comprises a drive system (32, 33, 18) for: - controlled positioning of the first column in relation to the second column, in parallel with the first horizontal axis, and - controlled positioning of the first workpiece holding device in relation to the first column, in parallel with the first horizontal axis. - controlled positioning of the first column in relation to the second column, in parallel with the first horizontal axis, and - controlled positioning of the first workpiece holding device in relation to the first column, in parallel with the first horizontal axis.