Computational fluid dynamic methods based on a finite-element technique were applied to the study of (1) competition of flows in the inferior and superior venae cavae in total cavopulmonary connection, and (2) competition between flow in the superior vena cava and forward flow from a stenosed pulmonary artery in bidirectional cavopulmonary anastomosis. Models corresponding to various degrees of offsetting and shape of the inferior vena caval anastomosis were simulated to evaluate energy dissipation and flow distribution between the two lungs. A minimal energy loss with optimal flow distribution between the two lungs was obtained by enlarging the inferior vena caval anastomosis toward the right pulmonary artery. This modified technique of total cavopulmonary connection is described. A computational model of the operation was developed in an attempt to understand the mechanisms of postoperative failure. In tight pulmonary artery stenosis (75%), the pulsatile forward flow is primarily directed to the left pulmonary artery, with little influence on superior vena caval pressure and the right pulmonary artery. Pulsatile forward flows corresponding to 15%, 30%, 45%, and 60% of the systemic artery output increased the mean pulmonary artery and superior vena caval pressures by 1, 1.7, 2.4, and 3.6 mm Hg, respectively. Although the modeling studies were not able to determine the cause of postoperative failure, they emphasize the impact of local geometry on flow dynamics. More simulations are required for further investigation of the problem.