We propose an arterial network model based on 1D blood hemodynamic equations to study the behavior of different vascular surgical bypass grafts in case of an arterial occlusive pathology: an obliteration or stenosis of the iliac artery. We investigate the performances of three different bypass grafts (Aorto-Femoral, Axillo-Femoral and cross-over Femoral) depending on the degree of obliteration of the stenosis. Numerical simulations show that all bypass grafts are efficient since we retrieve in all cases the normal hemodynamics in the stenosed region while ensuring at the same time a global healthy circulation. We analyze in particular the Axillo-Femoral bypass graft by performing hundreds of simulations by varying the values of the Young's modulus [0.1−50 MPa] and the radius [0.01−5 cm] of the bypass graft. We show that the Young's modulus and radius of commercial bypass grafts are optimal in terms of hemodynamic considerations. The numerical findings prove that this approach could be used to optimize or plan surgeries for specific patients, to perform parameter's statistics and error propagation evaluations by running extensive simulations, or to characterize numerically specific bypass grafts.