The processes of ion back-scattering from the surfaces of various targets have been studied by means of the computer simulation (different modifications of the Monte-Carlo method). The analysis of the experimental and calculated data allows proposing the mechanism explaining the target temperature dependence of the shapes of the back-scattered ion spectra. The formula satisfactorily describing the dependence under study has been developed. (C) 2002 Elsevier Science B.V. All rights reserved.