Pulmonary hypertension (PH) characterized by elevated mean pulmonary arterial pressure (mPAP) impairs coronary flow that leads to right ventricular (RV) failure, however, the underlying mechanism that controls the transition from compensated to decompensated RV failure remains poorly understood. To address this, we developed a computational model that integrates coronary perfusion in the major coronary arteries with a biventricular mechanics model in a closed-loop systemic and pulmonary circulations, to quantify the effects of acute and chronic PH on heart function and coronary blood regionally and transmurally cross the myocardium. The model predicts a reduction in coronary flow in the right ventricular free wall (RVFW) and septum during acute PH due to elevated intramyocardial pressure in the RV, which is higher in the endocardium than that in the epicardium. The model also predicted that the coronary flow in the left ventricular free wall (LVFW), septum, and RVFW is reduced in chronic PH due to diminished perfusion pressure. The computational model predictions suggest that the impairment of right coronary flow in chronic PH increases ischemic risk through reduced left coronary perfusion, which further affects the left ventricular (LV) function. These findings indicate the effects of PH on regional coronary flow may determine the transition from compensated to decompensated RV failure.