The large outflow channels of Chryse Planitia, Mars, are thought to have been carved by floodwaters discharged from an aquifer beneath a confining cryosphere. However, conventional models of groundwater flow require optimistically high permeabilities to produce, in a single flooding event, the discharge rates and volumes inferred from channel morphology. Additionally, discharge likely ceased upon refreezing of chaotic terrain fractures carrying it to the surface, further limiting the volume of water produced in a single flood. It is thus probable that multiple surface discharge events were required, and we quantify this hypothesis with regional groundwater simulations. Each discharge event is triggered by cryosphere disruption due to superlithostatic hydraulic head at the channel source region and is terminated by cryosphere fracture refreezing. Before the next event, head is allowed to recover with the aid of distal aquifer recharge constrained by previous global groundwater models. Our baseline model, which emulates the source region of Kasei Valles, yields a minimum of 2900 flooding events even for high depth‐averaged aquifer permeabilities corresponding to near‐surface values of 10−9m2. Although fewer events are required for other circum‐Chryse channels, formation by a single flood remains improbable. We suggest that unrealistically high numbers of floods may be circumvented by an alternative model involving the local ponding of surface discharge to form standing bodies of water. Episodic failure of these bodies produces flood outbursts which erode the channels.