In this paper we address the two-class classification problem within the tensor-based framework, by formulating the Support Tucker Machines (STuMs). More precisely, in the proposed STuMs the weights parameters are regarded to be a tensor, calculated according to the Tucker tensor decomposition as the multiplication of a core tensor with a set of matrices, one along each mode. We further extend the proposed STuMs to the Σ/Σ w STuMs, in order to fully exploit the information offered by the total or the within-class covariance matrix and whiten the data, thus providing in-variance to affine transformations in the feature space. We formulate the two above mentioned problems in such a way that they can be solved in an iterative manner, where at each iteration the parameters corresponding to the projections along a single tensor mode are estimated by solving a typical Support Vector Machine-type problem. The superiority of the proposed methods in terms of classification accuracy is illustrated on the problems of gait and action recognition.