Floodwaters on Mars likely originated from aquifers confined below a cryosphere. We use an analytical solution to examine freezing-induced pressurization as a mechanism for releasing groundwater. The results suggest that freezing of an aquifer of global extent under the optimal conditions, i.e., perfectly confined and with low compressibility and high permeability relative to the terrestrial analogs, can release enough floodwaters to carve an individual outflow channel, but not to explain the large total flood volume required to form the all of the outflow channels. It can also produce discharges comparable to those required for carving the outflow channels by repeated floods.