Many earth dams around the world are located in zones characterised by moderate to high seismicity. Their seismic stability can be particularly critical for the safety of the areas in the downstream side and therefore an in depth understanding of their response during earthquakes is required. This thesis describes a numerical study related to both the seismic response and analysis of earth dams using the finite element method. In the first part of the thesis, the effect of the upstream reservoir hydrodynamic pressures on the elastic seismic response of dams is explored. Firstly, a methodology is proposed in which the reservoir domain is modelled with finite elements focusing in particular on the accurate prediction of the hydrodynamic pressures on the upstream dam face. Secondly, a parametric study of dam-reservoir interaction is carried out to examine the effect of the reservoir on the seismic response of dams. The second part of the thesis is concerned with the nonlinear seismic behaviour of earth dams. Firstly, a well-documented case study, the La Villita dam in Mexico, is analysed in order to validate the numerical model and a good agreement is obtained between the recorded and predicted data. Subsequently, using as a reference the calibrated model, parametric studies are performed in order to obtain a better insight into the dynamic response and analysis of earth dams. The latter studies provide a means to assess the effect of different modelling considerations on the seismic analysis of dams.