Twin screw extruders are common for mixing and compounding of different polymers and additives in the production of materials with enhanced properties. However, the flow field and resulting mixing that occur inside these extruders are not well understood. For gaining a better understanding of the flow phenomena that take place during these operations, computer simulation can be used; however, due to the complexity of the moving boundaries in the twin screw extruder this is not an easy task. Using the boundary element method (BEM), which is the method of choice for moving boundary problems, the flow field, pressures, stress, and strains can be computed at every time step. With this information, the quality of mixing can be determined quantitatively and allows the engineer to modify the geometry of the screws for optimal mixing conditions. In this article, the boundary element method is used to analyze and compare mixing effectiveness of various geometries of the twin screw extruder.