The effects of the discrete cellular structure on propagation of electrical excitation in cardiac muscle were studied in a one-dimensional fiber model containing a periodic intercalated disk structure. Globally, the macroscopic velocity of propagation follows the behavior associated with propagation in a continuous tissue (except for high values of disk resistance). In addition, the computed spatial extracellular potential along the fiber is a smooth biphasic waveform and does not reflect the underlying discrete cellular structure of the tissue. Other results of the simulations demonstrate the discontinuous nature of propagation and the importance of the structure in arrhythmogenesis. Vmaxdisplays a biphasic behavior as a function of increasing intercalated disk resistance. An initial "paradoxical" increase in Vmax(with a simultaneous decrease in conduction velocity) is followed by a decrease that leads to decremental propagation and conduction block. The time constant of the foot of the action potential (±toot) increases monotonically with increasing intercalated disk resistance. An increase in the leakage current to extracellular space brings about a significant decrease in the action potential duration and a loss of the plateau. This major effect is accompanied by a relatively smaller decrease in conduction velocity. Collision of two activation wavefronts results in a significant (100%) increase in Vmaxand a very small (0.6%) decrease in ±toot.