The ancient outflow channels on Mars exhibit fossil flow patterns similar to current flow patterns in terrestrial desert regions eroded by wind. We have modeled outflow channel formation by a cascade process in which sand-sized particles produced by rock weathering in the chaotic terrain 'source areas' of the outflow channels were transported by the wind across the adjacent plateau surfaces, and sand blasting and deflating the surface. Comparisons of model predictions with photogeologic data suggest that rates of rock breakdown by physical and chemical action along the channels during the channel-forming era must have been much higher than they have been on similar terrains formed after the channel era ended. A tenuous atmosphere, comparable to the present one, could have transported materials sufficiently rapidly to excavate outflow channels in about 106 years. However, there may be difficulties in explaining how abrading particles could survive high-velocity impacts in a thin atmosphere over the many hundreds or even thousands of kilometers that they were transported in outflow channels. It is difficult to avoid the conclusion that a climate change affecting rock breakdown rates, atmospheric density, or both occurred early in Martian history to end the era of outflow channel formation. Particulate materials generated during this era may be important components of the north circumpolar dune field and the polar layered deposits.