Abstract: The machine has a tube extrusion head, an entrainment device arranged downstream of the extrusion head along the extrusion direction, and a device for checking the outer diameter of the tube. The device for checking the outer diameter of the tube includes a pneumatic gauge which is interposed between the extrusion head and the entrainment device and is operatively connected to an electronic control unit which acts on the entrainment device to adjust the tube entrainment speed as a function of the outer diameter of the tube to be obtained.