The invention relates to the processing of thermoplastic materials by extrusion, in particular for the manufacture of flexible tubular products, especially thick (more than 300 microns thick) single or multilayer sleeve polymer films of small diameter. The proposed method consists in the fact that during the launch period, the formed blank of the sleeve polymer film through the annular extrusion head is blown with compressed air and simultaneously cooled during contact with the wall of the upper part of the calibration device, located above the free surface of the water in the water bath, pass the pre-cooled blank of the sleeve polymer film through the lower part of the calibration device immersed in the water bath and connected to the vacuum line. After filling the initial section of the cooled polymer bag film into the gap between the pulling rollers, the compressed air supply inside the polymer bag film is turned off, forming a vacuum in the water bath. The cavity of the polymer film is connected to the atmosphere through the ring extrusion head. The device for calibrating the tubular product on the outer diameter contains a cooled tubular body with two consecutive sections, the first of which is made with a solid wall, and the second – with at least one hole in its wall connected to the vacuum line. Both sections of the tubular body have a working inner surface of the same diameter. In this case, the tubular body is located vertically under the extrusion head in a water-filled water bath under vacuum. The cavity of the tubular body through the extrusion head with the help of control and shut-off valves is connected to the pneumatic line and the atmosphere.