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This paper discusses the local approach of fracture using damage mechanics concepts to evaluate the seismic response of concrete gravity dams. A constitutive model for plain concrete, subjected to tensile stresses, is presented. The meshdependent hardening technique is adopted such that the fracture energy dissipated is not affected by the finite element mesh size. The model is implemented in conjunction with the Hilber, Hughes Taylor alpha algorithm for time marching. Koyna dam is utilized to validate the proposed formulation. The importance of initial damage prior to the advent of an earthquake is also investigated. A 60 m concrete gravity dam is therefore selected and subjected to ground motion typical of eastern North America. Five scenarios of initial damage are presented and the results confirm the importance of accounting for the initial state for the seismic safety evaluation of an existing dam.