The failure of synthetic small-diameter vascular grafts has been attributed to a mismatch in the compliance between the graft and native artery, driving mechanisms that promote thrombosis and neointimal hyperplasia. Additionally, the buckling of grafts results in large deformations that can lead to device failure. Although design features can be added to lessen the buckling potential, the addition is detrimental to decreasing compliance (e.g., reinforcing coil). Herein, we developed a novel finite element framework to inform vascular graft design by evaluating compliance and resistance to buckling. A batch-processing scheme iterated across the multi-dimensional design parameter space, which included three parameters: coil thickness, modulus, and spacing. Three types of finite element models were created in FEBio for each unique coil-reinforced graft parameter combination to simulate pressurization, axial buckling, and bent buckling, and results were analyzed to quantify compliance, buckling load, and kink radius, respectively, from each model. Importantly, model validation demonstrated that model predictions agree qualitatively and quantitatively with experimental observations. Subsequently, data for each design parameter combination were integrated into an optimization function for which a minimum value was sought. The optimization values identified various candidate graft designs with promising mechanical properties. Our investigation successfully demonstrated the model-directed framework identified vascular graft designs with optimal mechanical properties, which can potentially improve clinical outcomes by addressing device failure. In addition, the presented computational framework promotes model-directed device design for a broad range of biomaterial and regenerative medicine strategies.