We calculated the steady-state annular extrudate swell of polymer melts through flow geometries encountered in processes used to control parison thickness. A streamline-upwinding finite element method with an under-relaxation for the rate of deformation tensor was used. The Giesekus model was employed as the constitutive equation. An operation that widens the die gap is appropriate for the control of parison thickness corresponding to the change of die gap width. However, a control process that decreases the die gap width is not useful, because the parison thickness does not correspond to the die gap width. Furthermore, thickness swells change strikingly with the Weissenberg number. It; is difficult to control the parison outer diameter in the case of a converging die, because the change of the outer diameter swell becomes large with increasing Weissenberg number. In the case of a diverging die, the changing value of the outer diameter swell is smaller than that in the case of a converging die.