Atherosclerosis of the human arterial system produces major clinical symptoms when the plaque advances to create a high-grade stenosis. The hemodynamic shear rates produced in high-grade stenoses are important in the understanding of atheromatous plaque rupture and thrombosis. This study was designed to quantify the physiologic stress levels experienced by endothelial cells and platelets in the region of vascular stenoses. The steady hemodynamic flow field was solved for stenoses with percent area reductions of 50, 75, and 90 percent over a range of physiologic Reynolds numbers (100-400). The maximum wall shear rate in the throat region can be shown to vary by the square root of the Reynolds number. The shear rate results can be generalized to apply to a range of stenosis lengths and flow rates. Using dimensions typical for a human carotid or coronary artery, wall shear rates were found to vary from a maximum of 20,000 s-1 upstream of the throat to a minimum of -630 s-1 in the recirculation zone for a 90 percent stenosis. An example is given which illustrates how these values can be used to understand the relationship between hemodynamic shear and platelet deposition.