The Tucker3 method, proposed by Leyard Tucker en 1966, is identified as a technique designed to three-mode data analysis and is considered a generalization of the Principal Component Analysis (PCA) and the Singular Value Decomposition (SVD). This method uses matrix operations and decomposition procedures to estimate model parameters and its corresponding graphic representation in spaces of lower dimension to the original data array. By this method it is possible to explain information of a three-mode data set summarizing the associate entities through a few components, and to describe the possible interactions between the three sources of variation in the data using one central array. In this paper theoretical principles and the analytic supports for this method are presented and exemplified using hypothetical data.