During earthquakes tensile stresses in concrete darns may exceed the tensile strength of concrete. This study examines the earthquake response of gravity dams due to the non-linear behavior of concrete. For this purpose, Drucker-Prager criterion is used. The linear interaction between the dam and compressible water is included. In the finite element analysis of the two media the Lagrangian formulation was used. For numerical analysis, the earthquake response of Pine Flat gravity dam monolith has been studied. Linear and non-linear responses have been compared. A rigid foundation has been assumed for the dam and the effect of alluvium and sediments in the bottom reservoir on the response has been neglected.