In this talk we consider the Virtual Element Method applied to linear elasticity problems. In particular we focus our attention on mixed 2D/3D schemes based on the Hellinger-Reissner principle. As it is well-known, imposing both the symmetry of the stress tensor and the continuity of the tractions at the inter-element is typically a great source of troubles in the framework of classical Galerkin schemes, such as the Finite Element Method (FEM), for instance. We exploit the great flexibility of VEM to present an alternative to FEM, which provide symmetric stresses, continuous tractions and is reasonably cheap with respect to the delivered accuracy. In this talk, we detail the ideas which led to the design of our VEM scheme, we state the theoretical results, we show some applications, and we present several numerical tests to assess the performance of our approach.