Monte-Carlo methods are well suited to characterize events of which associated probabilities are not too low with respect to the simulation budget. For very seldom observed events, these approaches do not lead to accurate results. Indeed, the number of samples are often insufficient to estimate such low probabilities (at least 10 +2 samples are needed to estimate a probability of 10 − with 10% relative deviation of the Monte-Carlo estimator). Even within the framework of reduced order methods, such as a reduced basis approach, it seems difficult to accurately predict low probability events. In this paper we propose to combine a cross-entropy method with a reduced basis algorithm to compute rare events (failure) probabilities.