Patients with end-stage renal disease (ESRD) are usually treated by hemodialysis (HD) while waiting for kidney transplant. A common device for vascular access is arteriovenous graft (AVG). However, AVG failure induced by thrombosis has been plaguing dialysis practice for decades. Current studies indicate that the thrombosis is caused by intimal hyperplasia (IH) which is triggered by the abnormal flows and forces (e.g. wall shear stress) in the vein after AVG implant. Due to high level of complexity, in almost all of the existing works of modeling and simulation of the blood-flow vessel-AVG system the graft and blood-vessel are assumed to be rigid and immobile. Very recently we have found that the compliance of graft and vein can reduce flow disturbances and lower wall shear stress (WSS) (Z Bai and L Zhu, Computers & Fluids 181, pp. 403-415, 2019). In this paper, we apply the compliant model to investigate possible effects of several dimensionless parameters (AVG graft-vein diameter ratio R gv , AVG attaching angle θ, flow Reynolds numbers Re, and native vein speed V v ) on the flow and force fields near the distal AVG anastomosis at low Reynolds numbers (up to several hundreds). Our computational results indicate that the influences of the parameters R gv , θ, and Re lie largely on the graft and the influence of V v lies largely on the vein. In any case, the wall shear stress (WSS),