In this paper we introduce the literature on regression models with tensor variables and present a Bayesian linear model for inference, under the assumption of sparsity of the tensor coefficient.We exploit the CONDECOMP/PARAFAC (CP) representation for the tensor of coefficients in order to reduce the number of parameters and adopt a suitable hierarchical shrinkage prior for inducing sparsity. We propose a MCMC procedure via Gibbs sampler for carrying out the estimation, discussing the issues related to the initialisation of the vectors of parameters involved in the CP representation.