Many particle-filled materials, such as powder/binder mixtures, are known to show slip phenomena at a solid wall. It is thus of great importance to characterize the slip phenomena for rheological data of particle-filled plastic materials and ultimately to introduce an appropriate slip modeling into the numerical simulations of the extrusion process. In order to simulate screw extrusion processes of such particle-filled materials, numerical analysis programs were developed via a finite element method and a finite difference method for quasi three-dimensional and two-dimensional flow models of extrusion processes, respectively, with the slip phenomena taken into account in terms of a slip velocity. The present paper presents detailed numerical methods to incorporate the slip velocity as a function of wall shear stress and discusses essential slip effects in the screw extrusion process using the slip-corrected and uncorrected viscosity data for both the two-dimensional flow and the quasi three-dimensional flow model. It was confirmed that the quasi three-dimensional result at the center line of the channel from the finite element analysis was in good agreement with the two-dimensional one from the finite difference analysis. Slip effects were found to be very significant on the overall flow behavior during the extrusion process from the numerical results based on viscosity data without the slip correction. These deviated from those based on the slip-corrected viscosity data, especially in analyzing the screw characteristics.