Reliability analysis is concerned with estimating the very small failure probability of physical systems. The reliability problem amounts to computing an integral characterised by a computationally expensive, implicitly defined, and high-dimensional performance function. In most practical applications, this integral is intractable to both analytical and numerical techniques. Therefore, specialised reliability methods have been developed. Modern approaches, such as sequential importance sampling [1] and the cross-entropy method [2] are efficient and widely applicable. However, when the performance function exhibits challenging topology, i.e. rapidly changing output or multiple local optima, such reliability methods can yield degenerate estimators of the probability of failure. This work proposes niching importance sampling, an approach that combines concepts that are familiar in the study of reliability analysis --such as Markov chain algorithms, importance sampling, and relative cross entropy minimisation-- with niching techniques taken from the field of evolutionary multimodal optimisation. The result is a highly robust estimator for the probability of failure, that can provide an understanding of the underlying geometry of a reliability problem. Niching importance sampling is tested in a series of numerical experiments and is shown to outperform other reliability methods on selected challenging performance functions.