A machine tool (1) for machining by chip removal, in which a machining head (2) operates while being positioned in a horizontal plane and is mounted on a vertical bed (3) to which it discharges the forces (F) by which it is axially stressed, this vertical bed (3) being connected to a supporting structure (4). The vertical bed (3) is pivoted on the supporting structure (4) and there are interposed between the vertical bed and the supporting structure one or more bars (5) whose axial length (L) can be varied by magnetostriction produced by electric currents whose characteristics are determined continuously by a control device (6) in such a way as to counteract the horizontal movements of the vertical bed (3), thus keeping the machining head (2) fixed with respect to the workpiece (7) which it is machining.