The governing field equations and boundary conditions are, therefore re-derived, aiming, first, at a clear and systematic formulation of the basic equations, separating, secondly, the steady-state and transient response and, thirdly, attempting to use (regular and singular) perturbation techniques in answering various questions of the state of stress and velocity in a nearly parallel-sided slab. Results are different from previous ones. In fact Budd's analysis of the transfer of the bedrock topography to the surface is paralleled with the striking result that filter functions do not indicate the existence of a preferred-wavelength transfer, but the results show a marked dependency on the steepness of the ice slope. As far as surface waves are concerned, the results of the kinematic wave theory are corroborated for surface elevations that are small compared with the thickness of the ice sheet and for very long waves. When these conditions are not satisfied surface-wave equations become non-linear and exhibit features similar to the Burgers equation. In all these equations diffusion is more significant for ice sheets than for glaciers (with larger mean inclinations).