A numerical study of the three-dimensional flow and heat transfer in a single-screw extruder for polymeric materials such as plastics is carried out. The mathematical model is considerably simplified by conceptually unwrapping the channel and fixing the coordinate system to the rotating screw. Despite this simplification, strong property variations, particularly in the viscosity, complicated cross-sections employed in practical systems, large viscous dissipation effects and non-Newtonian nature of typical extruded materials make the problem a very difficult one to model numerically. Therefore, the transport processes in the extruder channel are simulated by means of a finite-element scheme which employs marching in the down-channel direction. The cross-section of the channel is taken as the commonly used rectangular or self-wiping profiles. An experimental study is also carried out using Newtonian and non-Newtonian fluids in order to provide data for the validation of the numerical model and also to quantify possible recirculation in the channel. Numerical results are presented on the temperature and velocity fields, resulting shear effects, pressure rise, heat transfer rates and viscous heating. The comparisons with experimental results indicate good agreement. A strong recirculating flow is found to arise over the cross-section of the channel. It is shown that a three-dimensional modeling of the process is necessary to capture the effects of recirculation in the channel. However,the marching procedure considerably simplifies the model as well as the inclusion of property changes and chemical reactions.