The elimbing effect that occurs when a non‐Newtonian fluid is sheared between rotating concentric cylinders is investigated in detail. A theoretical foundation is established for directly relating the climbing phenomenon to the material functions of a simple fluid. A relationship is developed between the normal stress functions and experimentally measurable quantities associated with the free surface thereby permitting all three material functions to be determined from a study of the flow field in a concentric cylinder apparatus. As an experimental verification of the theory, the material functions of a solution of polyisobutylene in cetane were determined for shear rates between 4 and30 sec−1.A good comparison is obtained between these and other published results for this material.