Over a nondeformable and impermeable bed, the sliding law has to be a relationship between the bottom shear stress &tgr;b, the sliding velocity u, and the effective pressure N=pi-pw, where pi is the ice load and pw is the pressure in the interconnected water cavities. Three horizontal scales are recognized: 0.1m, 10 m, and 10 km. Classical theories consider the smallest scale; they are of dubious value because temperature ice is neither dry nor totally impermeable. The intermediate scale yields sliding laws to be used in glacier modeling; melting-freezong processes may then be ignored. For modeling large, cold ice sheets, the sliding law at the largest scale is n eeded; it is suggested that sliding occurs only when a bottom temperature layer exists. How to tackle non-Newtonian rheology is discussed. At the intermediate scale a microrelief model consisting of two superimposed ''bumpy profiles'' is favored. If the smaller one had bumps of equal height, &tgr;b would be double values, but this model is unrealistic (the ice avalanche at the Allalingletscher in 1965 may be explained otherwise). Therefore a model with the smaller bumps of unequal height is adopted. It yields an asymptotic sliding law at large sliding velocities &tgr;b=fN+cuN1-n, with f and c as adjustsble parameters. A third one has to be introduced at low velocities. Although the correct interpolation function between both extreme cases remains unknown, some qualitative results about kinematic waves are obtained. ¿ American Geophysical Union 1987