Although the phenomenon of extrudate swell has been the subject of many studies the last 50 years both experimentally, numerically and theoretically, it is still not fully understood. It is important to develop a method to predict the die swell based on rheological properties and the geometrical dimensions of the extrusion die for several polymer processing operations. In this paper, the K-BKZ model with the PSM damping function has been utilized in order to simulate the die swell of a very high molecular weight HDPE in capillary extrusion. The goal of this study is to assess the effect of various parameters involved in the K-BKZ constitutive equation on predicting die swell, namely the relaxation spectrum, “” (shear parameter in the damping function), “” (the extensional parameter in the damping function) and “” (the normal stress differences ratio parameter). Finally, the contributions of slip and the effects of the geometrical parameters of dies on die swell are also examined in detail.