This paper reexamines the analytical framework for the steady, fully developed two-dimensional now in shallow channels, typical of screw extruders, and provides comprehensive solution sets for the Carreau-Yasuda and the Ostwald-deWaele model fluids. An application example for polymethylmethacrylate (PMMA) is included to compare the relative merits of the two models under specific extrusion conditions. The Ostwald-deWaele model, standard in engineering practice, can produce gross misrepresentations of the flow in extruder channels. Particularly, when dealing with highly shear-sensitive polymers, n < 0.3, or polymers with extended Newtonian plateau, Lambda similar to 1, the Carreau-Yasuda model becomes preferable. The inclusion of the Carreau model does not necessarily add tb the complexity of the analysis.