A model system consisting of a cluster of 13 Ag atoms and n (n = 1,2,3) H2 molecules has been used to study, by ab initio methods, the structural and energetic characteristics of the chemi- and physisorption processes of H2 on a (100) surface of silver. The dissociative chemisorption of a first H2 molecule is analyzed in terms of hydrides formation and it is shown that several electronic states are interacting in the vicinity of the activation barrier leading to complex electronic processes. The energy of the physisorption interaction of the first H2 molecule for different orientations and that of further H2 molecules coming directly on top of the first chemisorbed one are determined with highly correlated wavefunctions. As for the (H2)(n)Cu13 system, already studied with similar approaches, it is found for the (H2)(n)Ag13 system that the physisorption energy of the second layer is enhanced by a factor close to two compared to that of the first layer due to dipolar interactions with the polarized surface. The physisorption energy of the third and further layers tends to the van der Waals H2/H2 interaction energy.