In a recent set of modeling studies we have developed a stochastic threshold model of auditory nerve response to single biphasic electrical pulses (Bruce et al., 1999c) and moderate rate (less than 800 pulses per second) pulse trains (Bruce et al., 1999a). In this article we derive an analytical approximation for the single-pulse model, which is then extended to describe the pulse-train model in the case of evenly timed, uniform pulses. This renewal-process description provides an accurate and computationally efficient model of electrical stimulation of single auditory nerve fibers by a cochlear implant that may be extended to other forms of electrical neural stimulation.