Investigating the causes of failure of Fontan circulation in individual patients remains challenging despite detailed combined inva-sive cardiac catheterisation and magnetic resonance (XMR) exams at rest and during stress. In this work, we use a biomechanical model of the heart and Fontan circulation with the components of systemic and pulmonary beds to augment the diagnostic assessment of the patients undergoing the XMR stress exam. We apply our model in 3 Fontan patients and one biventricular "control" case. In all subjects, we obtained important biophysical factors of cardiovascular physiology-contractil-ity, contractile reserve and changes in systemic and pulmonary vascular resistance-which contribute to explaining the mechanism of failure in individual patients. Finally, we used the patient-specific model of one Fontan patient to investigate the impact of changes in pulmonary vas-cular resistance, aiming at in silico testing of pulmonary vasodilation treatments.