We used control method inversions to determine the basal shear stress beneath the Ross ice streams where new high-resolution velocity data sets have recently become available. The inversion algorithm was adapted from an earlier viscous bed algorithm to allow solution for the basal shear stress corresponding to a weak plastic bed. We performed several experiments using synthetic data to determine the quality of the inversions. These experiments indicate that with high-quality surface elevation data (e.g., errors <5 m), the inversions are relatively robust with respect to errors in ice flow velocity and bed topography. The inversions are consistent with seismic and borehole observations and indicate that the Ross ice streams lie atop a bed that is nearly everywhere weak. In contrast, the tributaries feeding these ice streams overlie alternating patches of strong and weak bed.