The bidirectional cavopulmonary anastomosis is used as a staged procedure or a definitive palliation of univentricular hearts. It is often performed in the presence of an additional blood flow arising from the native pulmonary outflow tract. In this paper, the effects of the severity of the pulmonary outflow obstruction and the pulmonary arteriolar resistance are analysed with regard to the haemodynamics in the superior vena cava and the blood distribution into the lungs. A computer model has been developed, which can represent both the preoperative and the postoperative (systemic and pulmonary) circulations in a patient with a double-outlet univentricular heart. It is particularly detailed in the region of the large vessels and includes components that account for local three-dimensional effects due to the actual shape of the anastomosis. Results have indicated that the mean pressure in the superior vena cava increases from 8.2 to 19.2 mmHg with pulmonary arteriolar resistance ranging from 0.8 to 7.9 Woods units and pulmonary outflow obstruction ranging from 50 to 100%. The percentage flow distribution to the right lung has turned out to be heavily affected by the flow competition and has ranged from 43 to 50% of the total flow to the lungs in the systolic phase, and from 51 to 62% in the diastolic phase. The model allows routinely used clinical indices to be computed, as well as the evaluation of new indices, which is potentially helpful in the clinical assessment of postoperative haemodynamics (e.g. the right-to-left lung flow ratio and the superior vena cava-to-pulmonary flow ratio).