A one-dimensional numerical ice flow model is used to study the advance of a tidewater glacier into deep water. Starting with ice-free conditions, the model simulates glacier growth at higher elevations followed by advance on land to the head of the fjord. Once the terminus reaches a bed below sea level, calving is initiated. A series of simulations was carried out with various boundary conditions and parameterizations of the annual mass balance. The results suggest that irrespective of the calving criterion and accumulation rate in the catchment area, it is impossible for the glacier terminus to advance into deeper water (>300 m water depth) unless sedimentation at the glacier front is included. The advance of Columbia Glacier, Alaska, is reproduced by the model by including “conveyor belt” recycling of subglacial sediment and the formation of a sediment bank at the glacier terminus. Results indicate slow advance through the deep fjord and faster advance in shallow waters approaching the terminal moraine shoal and the mouth of the fjord.