This article proposes a supervised tensor-based learning framework for classifying volcano-seismic events from signals recorded at the Ubinas volcano, in Peru, during a period of great activity in 2009. The proposed method is fully tensorial, as it integrates the three main steps of the automatic classification system (feature extraction, dimensionality reduction, and classifier) in a general multidimensional framework for tensor data, joining tensor learning techniques such as the multilinear principal component analysis (MPCA) and the support tensor machine (STM). By exploiting the use of multiple multichannel triaxial sensors, operating simultaneously in two seismic stations, the tensor patterns are constructed as stations × channels × features. The multidimensional structure of the data is then preserved, avoiding the tensor vectorization that often leads to a feature vector with a large dimension, which increases the number of parameters and may cause the 'curse of dimensionality.'Moreover, the array vectorization breaks down the multidimensional structure of the data, which usually leads to performance degradation. The results showed a good performance of the proposed multilinear classification system, significantly outperforming its vectorial counterparts. The best result was obtained with the STuM classifier along with the MPCA.