PURPOSE: To eliminate the formation of small scratches or parting lines on the surface of a polyester tube, by mechanically vibrating an outer mandrel existent in contact with the outer surface of the polyester tube.

CONSTITUTION: A polyester tube 1 extruded by an extruder is carried to a blow drawing apparatus, while adjusting its temp. slightly below the optimum drawing temp. In said blow drawing apparatus, the polyester tube 1 is heated at a drawable temp. with a heater 8 provided in a blow pipe 5 existent in said polyester tube 1 for supporting an inner mandrel 3. A drawable compressed fluid is injected through an ejection opening 6 provided in the blow pipe 5 to draw the polyester tube 1. High-frequency electric energy is formed by a power supplier 13 and converted into mechanical oscillation by a converter 12 to vibrate a connected outer mandrel 11.