In this paper, a three-dimensional model of blood flow through a vessel with an asymmetric stenosis is developed. The governing equations are the usual Navier-Stokes equations for unsteady elliptic flows, and these equations are solved using PHOENICS, a computational fluid dynamics package which uses the Finite Volume technique. The model is studied for values of Reynolds number ranging from 100 to 1000 for four different degrees of stenosis. Results of pressure drops show good agreement with published results. The study also shows that the side of the wall with the stenosis experiences a higher shearing stress compared to the opposite side without any protuberance. The ratio of the peak shear stresses on the walls may be as high as 2.5 for Re = 100 to 1000, and varies only slightly with the Reynolds number.