PURPOSE: To obtain a tubular film excellent in transparency, by keeping hot or annealing a melted and extruded tubular body, then cooling quickly it, cooling further it, and exhausting the cooling air.

CONSTITUTION: The tubular body 5 that has been melted and extruded is passed through an annealing chamber 6 where it is kept hot and annealed, and then it is quickly cooled by cooling air blown from an air ring 7 attached closely to the annealing chamber 6 normally to the axis of the tubular film 5. Cooling is further facilitated by sub-cooling air from a sub-cooling air intake 10 positioned between the lower end of an air blow shaping cylinder 11 provided around the inflated tubular film circumference and the upper end of the air ring 7, and the cooling air is exhausted from a cooling air sub-exhausting port 13 between the upper end of the air blow shaping cylinder 11 and an air blocking plate 15 over the cylinder 11 and from a cooling air exhausting port 14 between the air blocking plate 15 and the tubular film, thereby a tubular body excellent in transparency can be obtained.