Rubber compounds are known to be very shear-thinning and possess a strong degree of viscoelasticity. A series of rheological measurements for an SBR rubber are carried out using a moving die rheometer for the characterization of storage and loss moduli and a high-pressure capillary rheometer in order to study the effect of different die characteristics and temperature. The flow simulations are performed for axisymmetric (capillary dies) extrusion. The flow simulations are performed using a viscous (Cross) and an integral (K-BKZ) rheological constitutive equation (the PSM model). The effect of capillary die angle ranging from 180o to 60o is examined and no vortex activity is found in a wide range of apparent shear rates (or flow rates). Also, the effect of rheological properties is investigated because this rubber compound exhibits massive stick-slip in the shear rate regions > 100 s-1. Some conclusions on the pressure drop in the capillaries are drawn regarding the ability of the integral K-BKZ model to capture the viscoelastic behavior of SBR rubber. It is difficult to predict pressure drops if a rubber compound exhibits flow instabilities even using viscoelastic fluid flow models.