A key processing step in all extrusion operations is pumping. Forcing the polymer resin through the die at the discharge end of the processing machine requires the extruder screw to generate pressure, which may develop at various levels in all functional zones depending on the design of the screw-barrel configuration. The total pumping capability is therefore determined by the geometry of the entire screw. When predicting the pumping capability of an extruder screw, the diverse geometrical conditions in each screw section mean that the validity of traditional models must be critically reexamined. The literature on extrusion provides numerous theories for the prediction of flow rate and pressure build-up in extruders, which can be categorized according to the representation of the screw channel. While most methods are based on the flat-plate approximation, only a few include the effect of channel curvature. Assuming flow of power-law fluids, this work compares the conveying characteristics of flattened and curved screw channels for two- and three-dimensional flows. By solving the governing equations for these flow situations, we demonstrate the distinctive differences between these modeling approaches. We further analyze the usefulness of each method in relation to the underlying screw geometry.