This research work is devoted to the development of a mathematical model for the simulation of the flow of polymer melts through the metering and die regions of single screw extruders. The sets of the governing equations (flow and energy) are solved using the finite element method. The power-law model is used to describe the non-Newtonian rheological behavior of the fluid. The standard Galerkin technique is used in conjunction with the continuous penalty scheme to solve the flow equations. Due to the low thermal diffusivity of the polymer melts, a streamline upwinding Petrov-Galerkin method is used to obtain convergent and stable results for the energy equation. This method is based on the extension of a previously developed scheme. The overall solution strategy is based on the Picard iterative scheme. Simulation results are obtained for the flow of a polypropylene melt through the metering and die zones of a laboratory scale extruder. To validate the proposed model, the results of the computer simulations are compared with experimentally measured mass flow rate and pressure profile. These comparisons show that there is very good agreement between the model predictions and actual data.