The present study shows that high-resolution medium energy ion scattering (MEIS) can determine the shape and size of two (2D: height below two atomic-layers) and/or three (3D) dimensional nano-clusters of gold, for example, grown on oxide supports. We synthesized a computer program to simulate MEIS spectra from 2D- and/or 3D-clusters approximated by an appropriate analytic function and from underlying substrates. The observed MEIS spectra are well reproduced assuming a partial sphere for 3D-islands. The height, diameter and areal occupation ratios for 2D- and 3D-clusters together with size fluctuation are taken as fitting parameters. The MEIS spectra measured at different scattering geometries allows derivation of a unique solution for the above fitting parameters. The lateral size and its fluctuation determined in such a way agree with those observed by a scanning electron microscope of a field emission type. This paper also presents the initial growth process of gold nano-clusters on reduced TiO2(1 1 0) substrates. (C) 2008 Elsevier B.V. All rights reserved.