Mixing is one of the main functions of screw extruders. In the analysis of mixing, there are two mixing mechanisms that need to be considered: distributive and dispersive mixing. It is well known that single screw extruders generally have poor dispersive mixing capability, even when dispersive mixing elements are incorporated into the screw design. This paper will discuss the requirements for dispersive mixing, current dispersive mixing elements used in single screw extruders will be analyzed, and the lack of efficient dispersive mixing will be explained. A new generation of dispersive mixing elements will be introduced for use in both single and twin screw extruders and internal mixers. A two and three dimensional flow simulation will be used to analyze the mixing performance of these new mixers. Experimental work on the new mixing elements will be presented in a follow-up paper; the results demonstrate that it is possible to achieve dispersive mixing on single screw extruders that is as good as what can be achieved on twin screw extruders. The implications of these results on the compounding industry will be briefly discussed.