Simulation of wavefront propagation in the whole heart requires significant computational resources. The growth of cluster computing has made it possible to simulate very large scale problems in a lab environment. In this work, we present computational results of simulating a reaction diffusion system of equations of various sizes on a Beowulf cluster. To facilitate comparisons at different spatial resolutions, an idealized ventricular geometry was used. The model incorporates anisotropy, fiber rotation, and realistic membrane dynamics to determine the computational constraints for the most detailed situations of interest. Three meshes with mesh spacings of 378μm, 238μm, and 150μm, corresponding to roughly 1M, 4M, and 16M nodes in the computational domain, were considered. The results show that good parallel performance is possible on a cluster up to 32 processors.