[en] Theoretical methods for description of the processes of physical surface sputtering of metals by the fast particles are reviewed. The Zigmund theory based on the solution of transport equations and some mathematical models describing the sputtering process is considered. The method of computerized mathematical simulation is shown to give the results more adequate to the experiment than the Zigmund theory. Fields of application of the analytical theory and different analytical models are revealed. It is shown why the accountancy of some factors affecting such as presence of impurities, radiation damage of the surface, nuclear processes, etc. is not still realized at present; possible ways of their accountancy are outlined. Use of the IMITATOR program complex for simulation of physical sputtering is suggested. Preliminary calculations conducted by means of the complex for the case of nickel sputtering by nickel ions are presented