This thesis investigates the changes in surface shape which Occur when solid surfaces are subjected to bombardment and erosion by Energetic ion beams. The aspects which are studied lay particular emphasis on the type of problems encountered in the electronics industry where ion etching is used for the production of micro-relief on many commercial devices. Ion etching is also used extensively in surface analysis using techniques such as Auger Electron Spectroscopy, X-ray Photoelectron Spectroscopy and Secondary Ion Mass Spectroscopy both for surface cleaning and composition-depth profiling.