A potential interaction between the local hemodynamics and the artery wall response has been suggested for vascular graft failure by intimal hyperplasia (IH). Among the various hemodynamic factors, wall shear stress has been implicated as the primary factor responsible for the development of IH. In order to explore the role of hemodynamics in the formation of IH in end-to-side anastomosis, computational fluid dynamics is employed. To validate the numerical simulations, comparisons with existing experimental data are performed for both steady and pulsatile flows. Generally, good agreement is observed with the velocity profiles whereas some discrepancies are found in wall shear stress (WSS) distributions. Using the same end-to-side anastomosis geometry, numerical simulations are extended using a femoral artery waveform to identify the possible role of unsteady hemodynamics. In the current simulations, Carreau-Yasuda model is used to account for the non-Newtonian nature of blood. Computations indicated a disturbed flow field at the artery-graft junction leading to locally elevated shear stresses on the vascular wall. Furthermore, the shear stress distribution followed the same behavior with oscillating magnitude over the entire flow cycle. Thus, distal IH observed in end-to-side artery-graft models may be caused by the fluctuations in WSS's along the wall.