In two of our previous investigations (see ) we proposed using the stress function to develop a rather simple analytical and numerical strategies for obtaining the flow fields and attributes of generalized Newtonian fluid models in tubes of circular and non-circular (or with multiple connectivity) cross sectional geometries. In this paper we return to those investigations where we examine the flow of power law fluids in tubes of elliptical cross sectional geometry using the stress function approach that we proposed in those investigations (particularly in ).