A simplified model of ice-sheet behaviour is described. It combines the assumptions of rapid ice flow, high viscous activation energy and realistic sediment-based sliding dynamics to form a non-linear diffusion-type equation which can display relaxation oscillations analogous to those of surging glaciers, and which may be relevant to large-scale surges of the Hudson Strait and Cabot Strait ice streams of the Laurentide ice sheet.When the physics of this model is applied to a laterally extensive unidirectional ice flow, such as that in the Siple Coast of Antarctica, an appropriate mechanism may exist for the spontaneous generation of ice streams.