In this chapter, the design and development of a computational model of the cardiovascular system is presented for patients who have undergone the Fontan operation. The model has been built from a physiological basis, considering some of the mechanisms associated to the cardiovascular system of patients with univentricular heart disease. Thus, the model allows the prediction of some hemodynamic variables considering different physiopathological conditions. The original conditions of the model are changed in the Fontan procedure and these new dynamics force the hemodynamic behaviours of the different considered variables. The model has been proved considering the classic Fontan procedure and the techniques from the lateral tunnel and the extracardiac conduit. The results compiled knowledge of several cardiovascular surgeons with many years of experience in such interventions, and have been validated by using other authors' data. In this sense, the participation of a multidisciplinary team has been considered as a key factor for the development of this work.