In recent years, the Virtual Element Method (VEM) has proven to be a powerful tool for the numerical approximation of complex problems in computational mechanics, particularly in geophysical applications. Its flexibility allows for the use of general polygonal and polyhedral meshes, including non-convex elements and hanging nodes, making it ideal for problems with irregular geometries. In this talk, we focus on linear poroelasticity problems that describe the interaction of elastic deformation and fluid flow in fully saturated porous media. Specifically, we propose a lowest-order Virtual Element Method for the three-dimensional fully mixed formulation of Biot's problem. The flexibility of Virtual Element technology enables us, in addition to its geometric advantages, to enforce the symmetry of the stress tensor directly in the discrete space without increasing its complexity. This makes VEM a valid alternative to the standard Finite Element Method. Moreover, the choice of the lowest order of accuracy is motivated by the low regularity of material parameters in the applications of interest, as well as the desire to minimize the number of globally coupled degrees of freedom. We present the method, the convergence and stability analysis, and numerically investigate the behavior of our approach by applying it to a more realistic scenario: the footing-step problem.