Numerical modelling is a powerful tool for the investigation of human blood flow and arterial diseases such as atherosclerosis. It is known that near wall shear is important in the pathogenesis and progression of atherosclerosis. When modelling arterial blood flow it is generally assumed that blood is Newtonian. In this paper, blood flow is modelled in a realistic two-dimensional carotid artery geometry in order to investigate this assumption and its effect on the measurement of near wall shear. The assumption is tested in stenosed and unstenosed geometries and the non-Newtonian blood is modelled using the Carreau-Yasuda model. It is found that the velocity and shear fields, particularly near the walls of the geometries, exhibit small differences in general (<5%) between Newtonian and non-Newtonian models, even in the stenosed geometry with peak differences of 13.6%. Thus, when using numerical modelling to study the haemodynamic influences on atherosclerotic progression, we can safely neglect the non-Newtonian nature of blood.