We report the structures of Ag-Cu and Ag-Ni bimetallic clusters and nanowires (NWs), which are well known as effective Ag-based catalysts, by using an effective semi-grand-canonical ensemble Monte Carlo method. The metal metal interactions are modeled by the second-moment approximation of the tight-binding potentials. The simulation results show that the Ag-Cu and Ag-Ni bimetallic nanomaterials, including clusters and NWs, possess core-shell structures at different compositions, in which the Ag atoms lie on the surface, while the Cu or Ni atoms occupy the cores of the clusters and NWs. It is found that the pentagonal multi-shell-type structure can be transformed into cylindrical multi-shell-type structures for Ag-Cu and Ag-Ni bimetallic NWs at 100, 300, and 500 K. On the other hand, with the increase of Ag mole fraction in the Ag-Cu and Ag-Ni bimetallic clusters, the Ag atoms occupy the surface shell first, then the interior shell, and finally the central sites of the clusters. It is also found that the initial shape, composition, and temperature have little effect on the core-shell structures of the bimetallic clusters and NWs. The formation of core-shell Ag-Cu and Ag-Ni bimetallic clusters and NWs is due to the fact that a single Ag impurity is favorable to be situated in the core of the Cu or Ni clusters and NWs.