This paper presents a numerical analysis of a novel external support device for coronary artery bypass graft (CABG). The analysis includes the fluid and the structural dynamics of vein grafts with and without an external support device (ESD). Six different vein grafts geometries were modeled under time-dependent physiological conditions. The hemodynamics and the stresses developed at the graft wall were analyzed on patient based geometries 12 months posttransplantation. Results: veins under constriction of ESD were associated with higher wall shear stresses, lower shear gradients, uniform flow and lower structural effective stresses. In conclusion, these findings suggest that constricted graft with ESD improves hemodynamic and structural factors which are correlated to graft failure following CABG procedure.