It is shown how previous analyses of the falling cylinder viscometer for Newtonian fluids can be extended to non-Newtonian fluids. Specific relations are given for the velocity of descent for several simple non-Newtonian viscosity functions. A differentiation procedure is presented whereby the non-Newtonian viscosity for a fluid can be deduced from velocity of fall measurements. In the course of the development, some useful approximate expressions for axial non-Newtonian flow in annuli are developed. Finally, a comparison of the Ellis and power law models is made by an analysis of the axial annular flow data of Frederickson and of McEachern.