The first stage of surgical treatment for hypoplastic left heart syndrome (HLHS) includes the creation of artificial systemic-to-pulmonary connections to provide pulmonary blood flow. The modified Blalock-Taussig (mBT) shunt has been the technique of choice for this procedure; however, a right ventricle–pulmonary artery (RV-PA) shunt has been introduced into clinical practice with encouraging but still conflicting outcomes when compared with the mBT shunt. The aim of this study is to explore mathematical modeling as a tool for describing physical profiles that could assist the surgical team in predicting complications related to stenosis and malfunction of grafts in an attempt to find correlations with clinical outcomes from clinical studies that compared both surgical techniques and to assist the anesthesiologist in making decisions to manage patients with this complex cardiac anatomy. Mathematical modeling to display the physical characteristics of the chosen surgical shunt is a valuable tool to predict flow patterns, shear stress, and rate distribution as well as energetic performance at the graft level and relative to ventricular efficiency. Such predictions will enable the surgical team to refine the technique so that hemodynamic complications be anticipated and prevented, and are also important for perioperative management by the anesthesia team.