An attempt is made to validate the hypothesis made by the authors (Phillips and Deutsch, Biorheology 12 (1975), 383.), that a four constant Oldroyd constitutive equation is sufficient to characterize the constitutive behavior of blood. The validation proceeds by the comparison of theoretical predictions with experimental results for the problem of stability to small disturbances in circular Couette flow. The paper describes the development of a unique Taylor-Couette device and the comparison for 40% hematocrit whole human blood. Elasticity is found to have a substantially stabilizing effect on blood behavior. The constitutive model is found to be quantitatively inadequate and some results toward a higher order quantitatively adequate model are presented. It is suggested that a stress relaxation time of ca. 3 sec and a strain rate retardation time of 0.75 sec may have some meaning, in a suitably defined average sense, for normal hematocrit human blood. The use of these values in qualitative descriptions of the behavior of blood in complex flow situations should be of value.