Deep brain stimulation (DBS) is an established therapy for movement disorders, but the fundamental mechanisms by which DBS has its effects remain unknown. Computational models can provide insights into the mechanisms of DBS, but to be useful, the models must have sufficient detail to predict accurately the electric fields produced by DBS. We used a finite-element method model of the Medtronic 3387 electrode array, coupled to cable models of myelinated axons, to quantify how interpolation errors, electrode geometry, and the electrode-tissue interface affect calculation of electrical potentials and stimulation thresholds for populations of model nerve fibers. Convergence of the potentials was not a sufficient criterion for ensuring the same degree of accuracy in subsequent determination of stimulation thresholds, because the accuracy of the stimulation thresholds depended on the order of the elements. Simplifying the 3387 electrode array by ignoring the inactive contacts and extending the terminated end of the shaft had position-dependent effects on the potentials and excitation thresholds, and these simplifications may impact correlations between DBS parameters and clinical outcomes. When the current density in the bulk tissue is uniform, the effect of the electrode-tissue interface impedance could be approximated by filtering the potentials calculated with a static lumped electrical equivalent circuit. Further, for typical DBS parameters during voltage-regulated stimulation, it was valid to approximate the electrode as an ideal polarized electrode with a nonlinear capacitance. Validation of these computational considerations enables accurate modeling of the electric field produced by DBS.