Patient-specific geometric factors together with traditional risk factors may aid the early identification of patients at high risk of developing carotid artery disease requiring surgical intervention. Recent studies have linked aspects of carotid geometry to the pathogenesis of internal carotid artery (ICA) stenosis. Abnormal wall shear stress (WSS) is found for large ICA angles. Low WSS is believed to correspond to plaque formation whereas high WSS may result in plaque rupture and clotting. Here, the meshless method, smoothed particle hydrodynamics, is used to simulate Newtonian flow through a clinical, rigid walled, carotid bifurcation. The resulting flow field and WSS are reported for a range of different ICA angles. Varying the angle without changing boundary pressure conditions produces minimal change in flow and WSS. Greater ICA downstream pressures appear important for maintaining well-behaved flow through the bifurcation by suppressing flow separation downstream of the stenosis resulting in more uniform wall stress.