To study the interaction of electrical and mechanical processes in the three-dimensional heart, we have developed a high-order finite element model of the rabbit ventricles and used it to simulate electrical propagation and the passive mechanical response to ventricular filling in transversely isotropic myocardium. Simulations of passive mechanics showed good agreement with experimental epicardial strains. These simulations were conducted on a multiprocessor parallel platform and performance was shown to scale well with the number of processors used. Electrical propagation was simulated using the collocation-Galerkin method on portions of the anatomical model in both unloaded and deformed states. These models provide a framework for investigating how cellular biophysics integrate into the function of the intact ventricles.