Results of glacier flow models and associated estimates of future sea level rise depend sensitively on the prescribed relation between shear stress and slip velocity at the glacier bed. Using a fully three‐dimensional numerical model of ice flow, we compute steady‐state sliding relations for where ice slips over a rock bed with three‐dimensional, periodic topography. In agreement with studies of two‐dimensional beds, water‐filled cavities that form down‐glacier from bedforms cause basal shear stress to peak at a threshold slip velocity and decrease at higher velocities (i.e., rate‐weakening drag). However, the shear stress magnitude and extent of rate‐weakening drag depend systematically on lateral topographic variations not considered previously. Moreover, steep up‐glacier‐facing slopes of bedforms can result in shear stress that increases monotonically over a wide range of slip velocity, helping to stabilize slip. These results highlight the potential variability of sliding relations and their likely sensitivity to the morphological diversity of glacier beds.