We use a Tight-Binding Ising Model (TBIM) with effective pair interactions depending on concentration able to reproduce the bulk phase diagram of Pt-Ag system and in particular its strong asymmetry as a function of composition. This system presents both an L1 1 ordered structure around equiconcentration and a wide miscibility gap on the Pt-rich side. Using Monte Carlo simulations in canonical and semi-grand canonical ensembles, we succeed in reproducing qualitatively the bulk phase diagram and we study the equilibrium configurations of the (111) and (100) surfaces, and truncated octahedron clusters. The infinite surfaces reproduce sensibly the bulk phase diagram except that they present a strong silver surface segregation limited to the top surface layer. The clusters behave differently due to the reduction of the miscibility gap when decreasing the cluster size and present two typical ordered phases related to the L1 1 phase: one characterized by pure concentric atomic layers starting from silver surface layer which extends up to the center of the cluster, and the other one at higher silver concentration where the L1 1 phase is perfectly oriented along one (111) direction of the cluster. The later one has already been reported by recent experiments [1].