A cochlear implant (CI) is an auditory prosthesis that enables hearing by providing electrical stimuli through an electrode array. It has been previously established that the electrode position can influence CI performance. Thus, electrode position should be considered in order to achieve better CI results. This paper describes how the electrode position influences the auditory nerve fiber (ANF) response to either a single pulse or low- (250 pulses/s) and high-rate (5,000 pulses/s) pulse-trains using a computational model. The field potential in the cochlea was calculated using a three-dimensional finite-element model, and the ANF response was simulated using a biophysical ANF model. The effects were evaluated in terms of the dynamic range, stochasticity, and spike excitation pattern. The relative spread, threshold, jitter, and initiated node were analyzed for single-pulse response; and the dynamic range, threshold, initiated node, and interspike interval were analyzed for pulse-train stimuli responses. Electrode position was found to significantly affect the spatiotemporal pattern of the ANF response, and this effect was significantly dependent on the stimulus rate. We believe that these modeling results can provide guidance regarding perimodiolar and lateral insertion of CIs in clinical settings and help understand CI performance.