Action potentials arising from retinal ganglion cells ultimately create visual percepts. In persons blind from retinitis pigmentosa and age-related macular degeneration, viable retinal ganglion cells remain, and the retina can be stimulated electrically to restore partial sight. However, it is unclear what neuronal elements in the retina are activated by epiretinal electrical stimulation. This study investigated the effects of cellular geometry, electrode to neuron distance, stimulus duration, and stimulus polarity on excitation of a retinal ganglion cell with an epiretinal electrode. Computer-based compartmental models representing simplified retinal ganglion cell morphology provided evidence that the threshold for excitation was lower when an electrode was located in proximity to the characteristic 90 degrees bend in the axon of the retinal ganglion cell than when it was located over a passing axon of the nerve fiber layer. This electrode-position-dependent difference in threshold occurred with both cathodic and anodic monophasic stimuli, with point source and disk electrodes, at multiple electrode-to-neuron distances, and was robust to changes in the electrical properties of the model. This finding reveals that the physical geometry of the retinal ganglion cells produces stimulation thresholds that depend strongly on electrode position. The low excitation thresholds near the bend in the axon will result in activation of cells local to the electrode at lower currents than required to excite passing axons. This pattern of activation provides a potential explanation of how epiretinal electrical stimulation results in the production of punctuate, rather than diffuse or streaky phosphenes.