Commercial extrusion blow moulding operations typically employ tapered or ovalized annular dies. The geometry of the tool and the theological properties of the molten polymer determine the swelling characteristics and resulting dimensions of the extruded parison. A parison that is too thick will result in excessive part weight and an unnecessary waste of resin. A parison that is too thin may blow out during the inflation stage or yield a part possessing inferior mechanical properties. The thickness swell of the annular extrudate is a consequence of the molecular orientation which develops as a result of the shear and extensional stresses that result from the deformation history experienced by the material in a specific die configuration. The thickness swell will also be influenced by the diameter swell of the parison. The diameter swell and parison shape are primarily influenced by the circumferential (hoop) stresses and gravitational forces acting on the parison. Optimization of the swelling behaviour can be accomplished through appropriate die design with the aid of a computer-based simulation. The effect of die inclination angle, die gap opening, die contraction ratio, and diverging section length on the swelling characteristics of a high-density polyethylene melt are systematically examined. Numerical computations of the profile shape and stress distributions have been obtained using a commercial finite element software package (POLYFLOW). The material behaviour has been represented by an integral-type K-BKZ constitutive equation. Whenever possible, the predicted results have been compared with experimental data obtained on a commercial extrusion blow moulding machine. It was found that the thickness swell increases with increasing die contraction ratio and decreases with increasing inclination angle from the vertical as well as with increasing length of the tapered section. The diameter swell is sensitive to changes in the die geometry. In the absence of gravitational body forces, the circumferential stresses cause contraction of the outer diameter of the parison downstream from the die in the case of diverging die geometries. However, a pronounced extrudate expansion was observed in the case of extrudates emerging from converging annular dies. A detailed examination of the stress field by means of computer simulation is particularly helpful in understanding the extrudate swell behaviour associated with geometrically-complex dies.