The seismic safety of an arch dam is analyzed by calculating fragility curves for different damage and failure mechanisms. The model includes fluid–structure–foundation interaction and considers contact and material type nonlinearities. The ultimate limit state (failure) is studied by means of a plastic-damage concrete model, especially developed for cyclic loadings. The time histories of the ground motions are generated randomly by means of Kanai–Tajimi filter. Moreover, ten parameters of the model are considered as random variables, including the water level. To the best knowledge of the authors, for the first time, water-level variability is accounted for in a probabilistic seismic analysis of a dam. It is studied if it is admissible to increase the efficiency of the Monte Carlo simulation (MCS) by assuming lognormal distributions for the fragility curves. In general, the aim of this work is to show the possibilities and difficulties of probabilistic seismic analysis tools when applied to a sophisticated mechanical model of a real structure.