Concrete hydraulic structures such as: Dams, Intake Towers, Piers and dock are usually recognized as" Vital and Special Structures" that must have sufficient safety margin at critical conditions like when earthquake occurred as same as normal servicing time. Hence, to evaluate hydrodynamic pressures generated due to seismic forces and Fluid-Structure Interaction (FSI); introduction to fluid-structure domains and interaction between them are inevitable. For this purpose, first step is exact modeling of water-structure and their interaction conditions. In this paper, the basic equation involved the water-structure-foundation interaction and the effective factors are explained briefly for concrete hydraulic structure types. The finite element modeling of two concrete gravity dams with 5 m, 150 m height, reservoir water and foundation bed rock is idealized and then the effects of fluid domain and bed rock have been investigated on modal characteristic of dams. The analytical results obtained from numerical studies and modal analysis show that the accurate modeling of dam-reservoir-foundation and their interaction considerably affects the modal periods, mode shapes and modal hydrodynamic pressure distribution. The results show that the foundation bed rock modeling increases modal periods about 80%, where reservoir modeling changes modal shapes and increases the period of all modes up to 30%. Reservoir-dam-foundation interaction increases modal period from 30% to 100% for different cases.