Metal clusters have been extensively investigated from both experimental and theoretical viewpoints. Besides the technological interest, the fundamental question of how the physical properties evolve from the small clusters toward the macroscopic crystal has stimulated this effort. For supported clusters one not only has to understand the interaction between the atoms in the cluster, but also the interaction of clusters with substrate. If the cluster-substrate interaction is strong, the cluster would most likely grow in two-dimensions as opposed to free clusters [1]. It is our aim to shed some light on the complex problem of stability of free and supported clusters. The total energies and equilibrium geometries of free and supported clusters are calculated using tight binding potential and embedded atom method. For some cases the first principles calculations, based on the KKR Green's function method developed for supported clusters [2] are performed. We demonstrate that bulk trends in metal cohesion are well reproduced by small clusters with octahedral symmetry, which defines a lattice fragment component of the fcc, bcc and hcp metal lattices. The local near-neighbor interactions are investigated in free and supported clusters. Magic numbers in supported clusters on the (001) surfaces of Cu, Ni, Pd, Ag, Pt and Au are compared with results for free clusters. We propose a new approach based on TB MD and KKR Green's function method to describe the interaction between different types of atoms on metal surfaces [3]. Results for small Co clusters on the Cu(001) surface are presented.