Deep brain stimulation (DBS) of the subthalamic nucleus (STN) is modeled to explore the mechanisms of this effective, but poorly understood, treatment for motor symptoms of drug-refractory Parkinsons disease and dystonia. First, a neural field model of the corticothalamic-basal ganglia (CTBG) system is developed that reproduces key clinical features of Parkinsons disease, including its characteristic 4-8 Hz and 13-30 Hz electrophysiological signatures. Deep brain stimulation of the STN is then modeled and shown to suppress the pathological 13-30 Hz (beta) activity for physiologically realistic and optimized stimulus parameters. This supports the idea that suppression of abnormally coherent activity in the CTBG system is a major factor in DBS therapy for Parkinsons disease, by permitting normal dynamics to resume. At high stimulus intensities, nonlinear effects in the target population mediate wave-wave interactions between resonant beta activity and the stimulus pulse train, leading to complex spectral structure that shows remarkable similarity to that seen in steady-state evoked potential experiments.