This study was undertaken with the aim of contributing to the risk evaluation of Vesuvius. We calculate the surface displacements due to an increase in pressure in a shallow reservoir and assess the mechanical instability of the volcanic edifice and of the feeding system caused by pressure on the reservoir's walls and by regional stresses. We consider axisymmetric models that take into account topography, gravity, homogeneous and heterogeneous country rocks, spheroidal magma chambers with different aspect ratios and variable depths, and subvertical intrusions from the top of the chamber to various depths. We impose both symmetric and asymmetric regional stresses increasing with depth as boundary conditions. The models are static. The ground deformation and the stress distribution are calculated, in the framework of linear elasticity, by a numerical finite element method. The surface displacements refer to an overpressure of 10 MPa. This value is considered an upper limit for the fracture of surrounding rocks. We find the maximum vertical displacements to be of a few centimeters in the most favorable case and the displacement gradients to be at the lower limit of measurability. To evaluate the mechanical stability, we calculate the stress distributions of a prolate ellipsoidal reservoir within a heterogeneous medium. We consider a total hydrostatic magmatic pressure starting from the value of 50 MPa at the reservoir's top and three regional stress regimes from symmetric tensile to asymmetric tensile to strike-slip. In the last two cases we use three-dimensional models. The criteria adopted for instability are (1) the development of tensile tangential stress and (2) the Navier-Coulomb criterion, in compression. In no case have we found instability near or on the wall of the reservoir, whereas the slope of the volcanic edifice exhibits a shear failure instability, which increases with greater regional stress anisotropy.¿ 1997 American Geophysical Union