In the present research die swell phenomenon is investigated for the viscoelastic polymer melts both experimentally and by developing a mathematical model in a circular die for high impact polystyrenes (HIPS), high density polyethylene (HDPE), low density polyethylene (LDPE) and linear low density polyethylene (LLDPE). Die swell is generally attributed to the fluid stress field when the fluid flows in a die. The Leonov-like equations as a conformational model are solved simultaneously with dynamic equation of momentum transfer to predict the stress field for a viscoelastic fluid in a circular die. The average molecular weight, the polymer relaxation time and the polymer mobility tensors are determined using the experimental measurements of shear viscosity. Then, based on those data, a model is developed. The results predicted by the model for flow stress field are then used to calculate die swell ratio by Tanner's analytical model. Die swell ratio is also found out experimentally using a capillary rheometer for the samples. Comparison of the die swell results predicted by the model and measured experimentally show very good agreement for the polymers.