Coronary flow patterns and pressure/flow relationships in coronary vessels with arterial stenoses are examined by using a model that combines the flow in the epicardial arterial tree with the intramyocardial perfusion. By using appropriate resistive elements, the model allows for the autoregulation of the vascular bed and for the development of coronary collaterals. Arterial flow predictions are compared to canine data. Coronary stenosis is simulated by a local pressure drop caused by a combination of viscous and inertial forces; stenosis with a constant cross-sectional area is compared to a dynamic stenosis in which the cross-sectional area is a function of the instantaneous transmural pressure. Simulation results predict that the normal phasic flow patterns in the epicardial arteries are unaffected up to 73% reduction in cross-sectional area, while the average flow remains unchanged up to 90% area reduction. At the critical level of 90% rigid stenosis, the autoregulation is saturated and the phasic nature of the arterial flow is severely damped. Dynamic stenoses demonstrate hysteresis loops of the instantaneous pressure/flow relationship. Theoretical predictions of local and global values are in excellent agreement with experimental measurements, indicating that the proposed approach can be used to realistically describe the coronary flow in the ischemic heart.