The prospects for the implementation of modern digital technologies based on artificial neural networks (ANN) in the nuclear facility safety analysis are considered and the review of works on this topic is presented. The review includes publications in which neural networks are used in experimental studies and their result processing in such areas as heat transfer and hydrodynamics in single-phase media, in phase transformations, and hydrogen safety. Computational methods of machine learning based on artificial neural networks are successfully used to identify the relationship between the input and output system parameters without building complex mathematical computational models as well as for systems in which processes are characterized by nonlinearity and data uncertainty. However, a unified approach to the substantiation and assessment of the applicability of such methods has not yet been formed. As a result of the analysis, the need is shown for special requirements in order to assess the applicability of these technologies and substantiation (verification and validation) of calculation models based on neural networks.