Flow stripes along the surface of rapidly moving ice streams are shown to be an expected reaction of a viscous medium flowing over an irregular bed, whenever the velocity at the bed is large compared to shearing through the thickness. The principal features of the process are as follows. At high basal speeds the ice acts as a strongly selective band-pass filter transmitting basal undulations on spatial scales of a few ice thicknesses very effectively to the surface. The decay of the short-scale features by diffusion is strongly retarded by horizontal stress gradients. Consequently, localized disturbances at the bed produce topographic effects on the surface that are advected long distances down-stream before decaying away. This mechanism may explain many of the flow stripes on active ice streams moving by rapid basal motion.