The flow of non-Newtonian fluids obeying the power-law relation through the mixing sections of a single-screw extruder is analyzed with a modified flow analysis network (FAN) method. Three types of mixing elements, the Maddock, the dulmage, and the blister ring elements, are studied. The Maddock and the blister ring elements are dispersive type elements. They generate high pressure drop, and yield a negative pressure gradient which indicates poor pumping capability. The flow fields are rather regular in these elements. On the other hand, the dulmage element is a distributive type element. It generates a low pressure drop, and yields a positive pressure gradient at low extrusion rate which indicates better pumping capability than the dispersive type elements. Extensive flow splitting and reorientation is observed in this element. The power-law exponent has significant effect on pumping characteristics. However, the overall flow patterns of Newtonian fluids and power-law fluids in these mixing elements are quite similar.