Cochlear implants (CIs) rehabilitate hearing impairment through direct electrical stimulation of the auditory nerve. New stimulation strategies can be evaluated using computational models. In this study, a computationally efficient model that accurately predicts auditory nerve responses to CI pulse train input was developed. A three-dimensional volume conduction and active nerve model developed at Leiden University Medical Center was extended with stochasticity, adaptation, and accommodation. This complete model includes spatial and temporal characteristics of both the cochlea and the auditory nerve. The model was validated by comparison with experimentally measured single fiber action potential responses to pulse trains published in the literature. The effects of pulse rate and pulse amplitude on spiking patterns were investigated. The modeled neural responses to CI stimulation were very similar to the single fiber action potential measurements in animal experiments. The model's responses to pulse train stimulation with respect to spatial location were also investigated. Adaptation was stronger at the borders of the stimulated area than in the center. By combining spatial details with long-term temporal components and a broad implementation of stochasticity a comprehensive model was developed that was validated for long duration electric stimulation of a wide range of pulse rates and amplitudes. The model can be used to evaluate auditory nerve responses to cochlear implant sound coding strategies.