Experiments in rat brain slice show that hyperpolarized subthalamic nucleus (STN) neurons engage in slow, regular burst firing when treated with an N-methyl-d-aspartate (NMDA) bath. A depolarization-activated inward current (DIC) has been hypothesized to contribute to this bursting activity. To explore the mechanism for STN burst firing in this setting, we augmented a previously published conductance-based computational model for single rat STN neurons to include both DIC and NMDA currents, fit to data from published electrophysiological recordings. Simulations show that with these additions, the model engages in bursting activity at <1 Hz in response to hyperpolarizing current injection and that this bursting exhibits several features observed experimentally in STN. Furthermore, a reduced model is used to show that the combination of NMDA and DIC currents, but not either alone, suffices to generate oscillations under hyperpolarizing current injection. STN neurons show enhanced burstiness in Parkinson's disease patients and experimental models of parkinsonism, and the burst mechanism studied presently could contribute to this effect.