In Parkinsons disease (PD), the beta band ([12 30] Hz) component of basal ganglia activity is pathologically high. Deep brain stimulation (DBS) is an effective treatment to suppress symptoms of PD and is known to suppress pathological beta activity. However, the mechanism underlying this effect is not completely understood. Here, we tested the circuital effects of DBS in a computational model of the basal ganglia network in dopamine-depleted condition mimicking PD. Our model reproduces suppression of beta pathological oscillations in the basal ganglia network induced by subthalamic nucleus (STN) DBS. Crucially, this occurs for realistic levels of DBS intensity only if we incorporate short-term plasticity in STN projections to their downstream targets. STN stimulation hampers beta oscillations in the subthalamo-pallidal beta loop. This induces a progressive dephasing between this loop and the striato-pallidal beta loop, which leads in turn to a network-wide suppression of beta oscillations. This is also reflected in a restoration of the balance between D1 and D2 firing rates, which was altered by dopamine depletion. Moreover, the model also reproduces the DBS-induced gamma activity associated with symptom recovery. Finally, we explored the circuital effects of a broad range of DBS parameters in suppressing beta oscillations, focusing on the clinically relevant range of 60-150 Hz stimulation. The model suggests that 60-80 Hz stimulation frequencies might achieve beta desynchronization for an intensity even lower than the one needed at the standard 130 Hz frequency. Overall, our model lays the ground for in-silico tests of a broad spectrum of stimulation patterns.