The materials of the rubber composites especially in tire tread extrusion processes, are known to show die swelling phenomena at the end of the extrusion die due to the viscoelastic properties. It is thus of great importance to predict the swelling phenomena by introducing an appropriate numerical modeling into the three-dimensional numerical simulations of the tire extrusion process. In addition, for multi-layer tire extrusion processes, three dimensional interfaces are not known in priori in between the different rubber materials inside the die. Therefore, in this numerical development, we have implement numerical algorithms for tracking the 3D surfaces of the moving surface on the swelling region and interfacial surfaces in multiple tire tread layers. Numerical simulation results of die-swelling and layer thickness distributions obtained by the current method developed are compared with the corresponding results obtained by using the commercial software in terms of accuracy and computation time for several different viscoelastic models.