Intimal hyperplasia (IH) has been cited as a major cause of vascular graft failure, which is associated with the hemodynamic conditions [1, 2]. Most of the earlier studies were concentrated at the distal anastomosis, therefore in this study computational methods were used to describe the blood motion in the proximal anastomosis models. Both steady and pulsatile flow conditions have been investigated. For steady flow cases, low velocity regions were found to appear on both the heels and the toes of the junction. The spatial extent of these low velocity regions was dependent on the graft Reynolds number as well as on the grafting angle and the flow rate ratio of the graft and aorta. For the pulsatile flow, a low velocity recirculating region was formed during the peak flow phase and the flow was reverted from the graft back to the aorta during the deceleration phase of the cycle. Wall shear stress distributions for various cases were also computed. A reasonable good agreement was found between the present results and the previous PIV measurements.