Young flood channels emanate from Cerberus Fossae, Mars. In order to determine whether subsurface aquifers can discharge water sufficiently fast to explain these flood features, I develop a model that couples groundwater flow in a sub-cryosphere aquifer with flow through a fissure that penetrates from the surface to the aquifer. The model is constrained by estimates of peak discharge, and the distance water flowed uphill from the fissure. Aquifer permeabilities similar to those of young basalt aquifers on the Earth, ~10-9 m2, can produce inferred discharges of 106 m3/s <Burr et al., 2002a> but probably require multiple floods to create the channels.