An extensive modeling study is presented on viscoplastic flows in the single screw extruder. An effective modeling procedure is developed, and fully three-dimensional Non-Newtonian FEM computations are performed to design the screw and die characteristics which may be implemented into the global model of the process. ANSYS Polyflow software is applied to model these viscoplastic flows. An analysis is performed for the flow with yield stress effects both in the screw and in the die. Screw characteristics and die characteristics are calculated and modeled for various viscoplasticity parameters. The effect of yield stress parameters on the extruder operation has been discussed.