Propagation of water-filled crevasses through glaciers is investigated based on the linear elastic fracture mechanics approach. A crevasse will penetrate to the depth where the stress intensity factor at the crevasse tip equals the fracture toughness of glacier ice. A crevasse subjected to inflow of water will continue to propagate downward with the propagation speed controlled primarily by the rate of water injection. While the far-field tensile stress and fracture toughness determine where crevasses can form, once initiated, the rate of water-driven crevasse propagation is nearly independent of these two parameters. Thus, rapid transfer of surface meltwater to the bed of a cold glacier requires abundant ponding at the surface to initiate and sustain full thickness fracturing before refreezing occurs.