Membrane-based simulations in cardiac electrophysiology involve the numerical solution of the cable equation, which is composed of three terms. The transmembrane current density, Im, is analogous to the divergence of the spatial current flow in a section of the myocardium. The Im term is balanced by the charging of the membrane capacitance and the active flow of ions across the membrane, Iion. In simulations which are membrane-based, Iion is represented by a Hodgkin-Huxley type system of ionic currents dependent on the transmembrane potential, and the time course for the action potentials. Since the evaluation of these terms is computationally expensive, most reports to date have been limited to analysis of one-dimensional propagation. The purpose of this study was to analyze a number of computational techniques for finite difference solutions of the cable equation in one-dimensional, two-dimensional and three-dimensional models. In the one-dimensional model, the computational expense associated with each term in the cable equation was determined. Simulations of activation only, and simulations of activation with repolarization were performed using all computational techniques described. Analogous simulations were then completed in a two-dimensional model using a subset of the computational techniques which demonstrated the greatest efficiency in the one-dimensional simulations. By employing those techniques which provided the greatest computational savings in the two-dimensional simulations of activation, it was then possible to complete a three-dimensional simulation in a model built from 28,977 elements in 14 minutes CPU time on an IBM 3090.