During the last hundred years, several theories have been proposed aimed at describing the shape adopted by glaciers and their rate of downhill flow. Geophysicists, however, still cannot agree on the precise explanation of the phenomenon, and the dominant cause controlling the sliding of glaciers. This might be due to pressure arising during melting, or alternatively it might be due to stress concentration. In the current work a simple one-dimensional mathematical model is derived and analysed that predicts the geometric shape of the glacier’s longitudinal cross-section due to the combined effects of the ice’s mechanical resistance and the bed’s roughness. The glacier’s flow rate is supposed sufficiently slow to justify neglect of changes in the configuration with respect of time.