In this study the hemodynamic analysis of complete coronary bypass graft with elastic walls and different percentages of stenosis are investigated numerically. Blood flow is considered Newtonian and unsteady. The objective of this study is to deal with the influence of the wall elasticity, flow pulsatility and stenosis percentage on the flow configuration, Wall Shear Stress (WSS) and rotational flows. By comparing the rigid and elastic wall results of WSS, it is concluded that WSS obtains lower values in toe, heel and bed of the host vessel under the bifurcation in the elastic mode, which is closer to reality. Also it is concluded that with increasing the stenosis percentage, the possibility of occurring rotational flow will increase. The maximum and minimum values of WSS are observed in the stenosis of 70%. From the pulsatility of flow, it is observed that unsteady flow shows more accurate results also velocity and WSS have lower values compared with the steady state results.