Coronary flow reserve (CFR) is markedly reduced in patients with severe aortic valve stenosis (AS) but the exact mechanisms underlying this impairment of CFR in AS remain unclear. Reduced CFR is the key mechanism leading to myocardial ischemia, symptoms and adverse outcomes in AS patients. The objective of this study was to develop an explicit mathematical model formulated with a limited number of parameters that describes the effect of AS on left coronary inflow patterns and CFR. We combined the mathematical V³ (ventricular-valvular-vascular) model with a new lumped-parameter model of coronary inflow. 1000 Monte-Carlo computational simulations with AS graded from mild up to very severe were performed within a wide range of physiological conditions. There was a good agreement between the CFR values computed with this new model and those measured in 24 patients with isolated AS (r = 0.77, p<10^-4). A global sensitivity analysis showed that the valve effective orifice area (EOA) was the major physiological determinant of CFR (total sensitivity index = 0.87). CFR was markedly reduced when AS became severe, i.e. when EOA was < 1.0 cm², and was generally exhausted when the EOA was < 0.5-0.6 cm². The reduction of CFR that is associated with AS can be explained by the concomitance of: (1) reduced myocardial supply as a result of decreased coronary perfusion pressure and (2) increased myocardial metabolic demand as a result of increased left ventricular workload.