In primary production/UGS context, geomechanical modeling is aimed at evaluating the system safety in terms of reservoir and cap rock integrity, induced subsidence/rebound and existing faults (re)activation. To this end a discretized model able to describe the volume of interest is usually constructed and numerical simulations are performed to assess the displacement of the mesh nodes and the stress variation. Traditionally such calculations are performed through the well-established Finite Element Methods (FEM). In the present work, the Virtual Element Method (VEM) a generalization of FEM to polyhedral meshes was tested on ad hoc constructed 3D models and results were compared against solution obtained from FEM simulation.