Thrombus formation over a ruptured atherosclerotic plaque cap can occlude an artery with fatal consequences. We describe a computational model of platelet transport and binding to interpret rate-limiting steps seen in experimental thrombus formation over a collagen-coated stenosis. The model is used to compute shear rates in stenoses with growing boundaries. In the model, moving erythrocytes influence platelet transport based on shear-dependent enhanced diffusivity and a nonuniform platelet distribution. Adhesion is modeled as platelet-platelet binding kinetics. The results indicate that observed thrombus growth rates are limited by platelet transport to the wall for shear rates up to 6000 s-1. Above 7000 s-1, the thrombus growth rate is likely limited by binding kinetics (10-4 m/s). Thrombus growth computed from these rate-limiting steps match the thrombus location and occlusion times for experimental conditions if a lag time for platelet activation is included. Using fitted parameters, the model is then used to predict thrombus size and shape at a higher Reynolds number flow consistent with coronary artery disease.