A theoretical study of the sensitivity of Pt L-3 x-ray absorption near edge structure (XANES) to the size and shape in small Pt-n clusters is reported. Calculations, based on a full multiple scattering, self-consistent field, real-space Green's function approach implemented in the ab initio FEFF8 code, show that XANES provides a characteristic signature of cluster shape. For example, the calculated white line intensity exhibits a large variation for small cluster sizes and geometry, but becomes independent of cluster size for large clusters. A strong polarization dependence of the white line is predicted for two-dimensional clusters. For three-dimensional clusters the polarization dependence is smaller, but can be used as a measure of the "flatness" of a cluster. A series of semirelativistic all-electron, full potential density functional calculations was also performed for several Pt-n clusters. These calculations show the existence of intrinsic static disorder in these clusters due to nonisotropic shrinkage. There is an expansion along the (111) direction, and a contraction in the other directions. Additional calculations for a model Pt-6 cluster in zeolite-LTL pore show that, except for additional broadening of the white line, all XANES features of the free clusters are qualitatively preserved.