A coronary artery bypass graft (CABG) enhances circulation to the heart muscle in patients with significant coronary artery disease. CABG involves grafting a healthy artery from one part of the body to the blocked coronary artery. In this work, we have performed the computational fluid dynamics (CFD) using ABAQUS finite element software to understand the effect of CABG on entirely or partially blocked coronary arteries. The effect of laminar flow was evaluated using the no-slip condition and considered the Reynolds number parameter using momentum and transport properties for the given geometric, material, and physical constraints. Based on the failure studies, we can minimize the failure of coronary arteries. Our model can help freeze optimal surgical guidelines for coronary bypass surgery such that the graft remains patent even after years of operation. The chance of failure of the heart can be minimized by the reduction in flow, velocity, and corresponding Reynolds number, accurate linear and angular positioning of the draft, and estimation of blockage size and shape. The CFD analysis of blood flow in the artery after grafting for various parameters like graft angle, blockage size, and position. At optimum graft angle, blockage position and size result in minimum velocity, and the corresponding Reynolds number lies in the artery's laminar region of blood flow.