In order to quantify the importance of non-Newtonian blood rheology on anastomotic flow patterns, the characteristics of Newtonian and non-Newtonian blood flows were compared in a 2-D, 45 degree end-to-side anastomosis model under both steady and unsteady flow conditions. All flows were assumed to be two-dimensional, and were simulated numerically using parameters consistent with blood flow in the femoral artery. A novel, purely viscous constitutive relation, based on a generalized form of the power law relation, was developed to model the non-Newtonian rheology of blood. The resulting wall shear stress patterns indicate that for the parameter values under consideration, non-Newtonian blood rheology has a significant effect on steady flow wall shear stresses, but no significant effect on unsteady flow wall shear stresses. Based on these and other simulations, a parameter is formulated that gives an indication of the importance of non-Newtonian blood rheology under a given set of flow conditions. In addition, an argument is presented for allowing the conclusions from this two-dimensional study to be extended to three-dimensional blood flow.