A methodology to construct patient-specific, anatomically and physiologically realistic finite element models of blood flows in stenosed carotid arteries is presented. Anatomical models of carotid arteries with stenosis are reconstructed from contrast-enhanced magnetic resonance angiography (MRA) images using a tubular deformable model along each arterial branch. A surface-merging algorithm is used to create a watertight model of the carotid bifurcation for subsequent finite element grid generation. A fully implicit scheme is used to solve the incompressible Navier-Stokes equations on unstructured grids in three-dimensions. Physiologic boundary conditions are derived from cine phase-contrast MRA flow velocity measurements at two locations below and above the bifurcation. The methodology was tested on image data of a patient with carotid artery stenosis. A finite element grid was successfully generated from contrast-enhanced MRA images, and pulsatile blood flow visualizations were produced. Visualizations of the wall shear stress distribution and of changes in both its magnitude and direction were produced. These quantities may become important in order to characterize healthy and diseased flow and wall shear stress patterns. We conclude that MRA can be used to obtain all the anatomical and physiologic data necessary for realistic modeling of blood flows in carotid arteries with stenosis. Our results confirm that image-based computational fluid dynamics techniques can be applied to the modeling of hemodynamics in carotid arteries with stenosis. These capabilities may be used to advance our understanding of the generation and progression of vascular disease, and may eventually allow physicians to enhance current image-based diagnosis, and to predict and evaluate the outcome of interventional procedures non-invasively.