In most polymer processes, the quality of the final part is greatly dependent on the melting, flow and mixing of the polymer. The optimization of the equipment and manufacturing process, as done today, is time consuming and expensive. It is often necessary to build complex flow visualization equipment, i. e., model extruders with transparent barrels, to qualify the flow during processes. Quantifying flow and heat transfer is an even more intimidating task. Furthermore, reproducing the properties of a particular blend from batch to batch can be extremely difficult. Obviously, these barriers make numerical simulation a viable alternative when optimizing and analyzing the extrusion process.Traditionally, when simulating polymer processes, the main concern of the engineer has been to accurately represent the material behavior using complex models. Although many problems still exist regarding polymer material models and will continue to be a field of research, today one can easily deal with the shear thinning behavior, temperature dependence and to some degree the viscoelasticity of polymers. In fact, to date a large number of processes have been realistically simulated in polymer processing ranging from mold filling with fiber orientation, shrinkage and warpage, to extrusion with viscoelastic effects. However, only a few fully threedimensional models of realistic processes have been solved. Simulating a fully three-dimensional process involves intensive labor, trying to accurately represent the geometry of the device and also requires large amounts of computation time and data storage. Obviously, computational demands have been reduced by the enormous increase in computational power available to the engineer at the desktop. However, the labor intensity and requirements of computer performance are multiplied by the added complexity of moving boundaries. Two types of moving boundaries are very common in polymer processing: moving free boundaries and moving solid boundaries.* Moving free boundary problems are encountered in such areas as mold filling, extrudate swell, coating problems, inside the extruder at the screw, to name a few. Solid moving boundaries are those where the actual cavity that con-* The name "moving solid boundary problems" for this category of problems was introduced by Prof . C . L .