Abstract: To explore multi-way data, different methods have been proposed. Here, we study the popular PARAFAC (Parallel factor analysis) model, which expresses multi-way data in a more compact way, without ignoring the underlying complex structure. To estimate the score and loading matrices, an alternating least squares procedure is typically used. It is however well known that least squares techniques suffer from outlying observations, making the models useless when outliers are present in the data. In this paper, we present a robust PARAFAC method. Essentially, it searches for an outlier-free subset of the data, on which we can then perform the classical PARAFAC algorithm. An outlier map is constructed to identify outliers. Simulations and examples show the robustness of our approach. [Copyright &y& Elsevier]