The geometric features of screws for both co- and counter-rotating twin screw extruders are developed from kinematic principles. It is shown that in co-rotating twin screw extruders there are more design constraints because the flight flank angle has to equal the angle of intermesh. This is not the case for counter-rotating twin screw extruders. The various geometries possible in the two types of extruders are shown. Although the geometries used for co-rotating extruders are well known, the geometries for counter-rotating extruders are not well known. In fact, some of the geometries possible with counter-rotating extruders have not yet been made commerically available. The implications of the geometric analysis on actual extruder performance is discussed in detail.