Many particle-filled materials, such as powder/rubber mixtures, are known to show slip and die-swelling phenomena at a die wall and at the free surface outside a die, respectively. Viscoelastic rheological properties induce the die swelling at the end of extrusion die. In addition, it is also of great importance to characterize the slip phenomena for rheological data of such materials and ultimately to understand an slip effects on the die swelling in the tire rubber extrusion process. The ultimate goal of this study is to design the optimal shape of die that produces the final extrudate product by taking into account the slip and viscoelastic effects. In this study, experiments have been carried out to predict the rheological data for viscoelastic rheological properties and slip phenomena. And we have experimentally examined the swelling shapes of several tire treads with the typical SBR rubbers. Then we have numerically simulated the die swelling for the rubber materials in terms of viscoelastic properties and slip parameters by using the commercial software. In the numerical analysis, we have used the nonlinear viscoelastic models of PTT and analyzed the die swelling pattern to compare with the experimental ones. The present paper presents and discusses detailed numerical results to understand the essential slip effects on the die swelling as a function of pressure gradient in the extrusion die.