The heart is a complex organ found in all vertebrates. It circulates blood throughout the body by cyclically contracting and relaxing. In an unhealthy heart, the pumping efficiency decreases, causing poor blood flow. What changes occur in a sick heart and how they affect its functioning is a subject of research. Much has been already understood about the electrophysiological changes that occurs in a sick heart. However, it is vastly unknown how these changes relate to mechanical dysfunction of the heart. A coupled electrophysiology and mechanics study of the heart may help answer some of the questions related to this. The focus of this dissertation is twofold. First we investigate efficient numerical techniques for solving the governing equations and discuss the convergence and accuracy of finite element electrophysiology simulation using the monodomain model. Secondly, we show the effect of mechanical deformation on stability of spiral waves, using combined electrophysiology and mechanics simulation.