In many situations, a researcher is interested in the analysis of the scores of a set of observation units on a set of variables. However, in medicine, it is very frequent that the information is replicated at different occasions. The occasions can be time-varying or refer to different conditions. In such cases the data can be stored in a three-way array or tensor. The Candecomp/Parafac and Tucker3 methods represent the most common methods for analyzing three-way tensors. In this work a review of these methods is provided and then this class of methods is applied to a three-way data set concerning hospital care data for a hospital in Rome (Italy) during fifteen years distinguished in three groups of consecutive years (1892-1896, 1940-1944, 1968-1972). The analysis reveals some peculiar aspects about the use of health services and its evolution along the time.