Abstract Alpine glacial landforms (such as U-shaped troughs, hanging valleys, and cirques) have been linked to the meltwater-modulated sliding motion of glaciers. Several of these alpine landforms are associated with characteristic length scales for width and spacing, indicating that the viscosity of ice exerts a first-order control on the processes responsible for their formation. Here we present the results of three-dimensional computational experiments focusing on the influence of higher order ice dynamical effects, such as horizontal stress gradients, on long-term glacial landscape evolution. Some of the experiments presented have highly simplified bed conditions; other experiments use topography from an existing mountain range as basis for simulating glacial erosion. The experiments demonstrate how gradients in horizontal stress play a primary role in scaling the bed shear stress of glaciers. We also demonstrate how higher order ice dynamics may influence the feedback between glacial sliding and erosion, hereby providing important stabilization mechanisms that prevent runaway effects associated with the steepening of longitudinal profiles and the formation of overdeepenings.