A shunt from the left ventricle to the left anterior descending artery is being developed for coronary artery occlusive disease, in which the shunt or conduit connects the the left ventricle (LV) with the diseased artery directly at a point distal to the obstruction. To aid in assessing and optimizing its benefit, a computational model of the cardiovascular system was developed and used to explore various design conditions. Computational fluid dynamic analysis for the shunt hemodynamics was also done using a commercial finite element package. Simulation results indicate that in complete left anterior descending artery (LAD) occlusion, flow can be returned to approximately 65% of normal, if the conduit resistance is equal for forward and reverse flow. The net coronary flow can increase to 80% when the backflow resistance is infinite. The increases in flow rate produced by asymmetric flow resistance are enhanced considerably for a partial LAD obstruction, since the primary effect of resistance asymmetry is to prevent leakage back into the ventricle during diastole. Increased arterial compliance has little effect on net flow with a symmetric shunt, but considerably augments it when the resistance is asymmetric. The computational results suggest that an LV-LAD conduit will be beneficial when the resistance due to artery stenosis exceeds 27 PRU, if the resistance is symmetric. Fluid dynamic simulations for the shunt flow show that a recirculating region generated near the junction of the coronary artery with the bypass shunt. The secondary flow is induced at the cutting plane perpendicular to the axis direction and it is in the attenuated of coronary artery.