A probabilistic seismic safety assessment is performed by means of Monte Carlo simulation.Emphasis is on the identification of response uncertainty as a result of the stochastic nature of ground motions in time domain.Especially, the relevance of low failure probabilities at moderate earthquakes is investigated.As application example an arch dam with nonlinear material properties and fluid-structure interaction is analysed.Exceedance probabilities for selected peak ground acceleration levels are obtained from a site-specific hazard curve.Stochastic ground motions are generated accordingly by a Kanai-Tajimi model.The fragility curve is calculated by performing Monte Carlo simulations.Its tail probabilities are estimated by a new extrapolation technique.