A computational model of blood flow in the heart is developed. The numerical method is based on the projection method for solving the time-dependent Navier-Stokes equations. This method has been used to study the flow of blood in both two-dimensional and three-dimensional models of the heart. The two-dimensional model has been used to study flows through the mitral valve, both natural and prosthetic. The three-dimensional heart model, based on anatomical dissections of the myocardial fiber paths, should be able to do in three dimensions the kinds of studies which have been successfully performed in two dimensions. Computer-generated videotapes showing results from both heart models are shown.