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Bounding probabilities of rare events in the context of computer experiments is an important concern in reliability studies. These rare events depend on the output of a physical model with random input variables. Since the model is only known through an expensive black box function, standard efficient Monte Carlo methods designed for rare events cannot be used. That is why a strategy based on importance sampling methods is proposed. This strategy relies on Kriging meta-modeling and manages to achieve sharp upper confidence bounds on the rare events probabilities. The variability due to the Kriging meta-modeling step is properly taken into account. The proposed methodology is applied to an artificial example and compared with more standard Bayesian bounds. Eventually, a challenging real case is analyzed. It consists in finding an upper bound for the probability that the trajectory of an airborne load will …