Summary: This paper deals with the problem of evaluating material elasticity through measurements of a material function such as the non-Newtonian viscosity. A brief summary is provided between relations involving several material functions. In particular, two methods for predicting the primary normal stress coefficient from the steady shear viscosity are examined in detail. These methods are due to Bird, Hassager, and Abdel- Khalik and to Wagner [e.g. \textit{S. I. Abdel-Khalik}, \textit{O. Hassager} and \textit{R. B. Bird}, Polym. Eng. Sci. 14, 859 ff. (1974)]. Experimental data are presented involving test fluids such as polymethyl methacrylate solutions, polystyrene solutions, and polyacrylamide solutions. Finally, a relation between the shear viscosity and the primary normal stress coefficient is discussed using the concept of the finitely extensible bead-spring chain model.