Hydrocarbon production, subsurface sequestration, and gas storage in exhausted reservoirs are a few anthropogenic activities involving the extraction or injection of fluids underground. As a consequence, the withdrawn/injected formation undergoes an effective stress change that may induce deep deformations propagating to the ground level with possible fault re-activations. The geomechanical parameters needed to simulate and predict the above processes can also be indirectly inferred by Interferometric Synthetic Apertur Radar (InSAR)-based techniques that are used to monitor the land surface displacements. In the present study, the InSAR measurements above two exhausted fields of the Po River plain, Italy, presently employed for seasonal gas storage, are used to develop, set up, and calibrate a transversely isotropic geomechanical model of the porous medium. It is shown that only assuming transverse isotropy allows for a satisfactory reproduction of both the vertical and horizontal displacements that cannot be simultaneously matched by a simpler isotropic model. Moreover, similar parameters prove correct for both the reservoirs, located about 30 km apart, providing evidence of the regional range of the above model applicability.