In a plasticating screw extruder, a polymer melt forms in the melting zone of the extruder. Pressurization of the molten polymer takes place in the melting and the metering sections so that the melt can flow through the restricted passage of the die and assume a desired shape. In a melt fed extruder, the throughput is governed by the pressure rise over the entire length of the extruder. The pressure developed in the screw channel may also be employed in rapid filling of molds, such as those in injection molding. When the geometry of the screw, the barrel temperature, and the die are selected, a unique set of operating parameters arise for a particular flow rate or screw speed. In the present study, numerical and analytical methods are used to calculate the transport in the extruder and the pressure drop in the die. An iterative numerical method based on solving the equations of motion and energy in the screw channel and a correction scheme to couple the die with the screw channel is discussed. The numerical algorithm is capable of handling an arbitrary variation of the viscosity of the polymeric fluid with the shear rate and temperature. The results obtained by simulating the fluid flow in the screw channel are compared with available numerical and experimental results in the literature, indicating good agreement. The performance characteristics of the extruder, for chosen thermal boundary conditions and screw geometry, are presented for different die geometries and different fluids. The important considerations that arise in the numerical simulation of the extrusion process are also discussed.