The carotid artery bifurcation is vulnerable to the buildup of atherosclerotic plaque. This buildup may lead to vessel occlusion or to embolism or plaque rupture. Numerical simulations of blood flow in severely stenotic vessels, when considered in conjunction with experimental and in vivo data, can contribute to the understanding of plaque rupture. The Navier-Stokes equations are solved in their finite-volume formulation for carotid bifurcation geometries based on surgically removed specimens. Aspects of plaque morphology are isolated so that their effect on flow patterns and fluid mechanical stresses may be independently evaluated; results suggest that a measure of such features as plaque asymmetry and surface irregularity may usefully complement percent stenosis in the diagnosis of vulnerable plaques. The resulting flows contain large recirculation zones and high spatial variations in wall shear. Even steady flows exhibit unsteadiness (e.g. vortex shedding) due to the complex plaque morphology. The computed flow patterns and fluid stresses in different atherosclerotic vessels may be compared to identify critical features of plaque geometry and “risk factors” for plaque rupture. In this way, numerical simulations can help determine the risk of plaque rupture posed by a particular plaque deposit.