During the rapid filling phase of the heart cycle, the internal volumes of the two ventricular cavities approximately double, while the intraventricular pressures rise typically only by an amount of less than 1 kPa. Such a small pressure increase cannot be the sole driving mechanism for the large inflow of blood associated with ventricular expansion during this period. Instead, the rapid filling phase is to be interpreted as being mediated primarily by the heart recoiling elastically from its contracted state, causing blood to be aspirated rapidly into the ventricles. In order to study the role of this mechanism, elastic finite element (FE) simulations of ventricular expansion were performed, taking into account the large deformations occurring during this period and the effective compressibility of the myocardium due to intramural fluid flow. Thereby, a realistic three-dimensional geometry derived from magnetic resonance imaging (MRI) measurements of both human ventricles was used. To validate our FE analyses, the results were compared with published measurements relating to the rapid filling phase of the human left ventricle. Our study shows that, under normal physiological conditions, ventricular aspiration plays a key role in the ventricular filling process.