In this monograph the basic methodologies for the non-linear seismic analysis of concrete dams are presented. The Finite Element Method is used to discretize the dam-foundation-reservoir ensemble, whereas the dynamic equations will be solved in the time domain according to implicit integration schemes, namely the Newmark method and the Hilber-Hughes-Taylor a method. For the non-linear problema predictor multicorrector algorithm is adopted. In view of the large scale computations inherent to dam analysis, a constitutive damage model for massive concrete is briefly presented. It incorporates two scalar damage variables with independent evolutions, simulating the degradation which occurs under tension or compression. Irreversible deformations are also accounted for, as well as concrete strain-rate effects. Attention is devoted to the numerical naire which arises from direct time integration, and to its control through the algorithmic dissipation provided by the a method, or by a stiffness proportional damping matrix which is updated to account for material degradation. Radiation damping to be provided at the artificial far boundaries located on the foundation and on the reservoir is also focused. Special care is devoted to the simulation of the reservoir. Numerical modelling of the hydrodynamic effect is discussed in detail, either by means of pressure or displacement formulations, or even through the technique ofthe added masses from Westergaard.