Continuous monitoring around drifts excavated in the Underground Research Laboratory (URL) of The French National Radioactive Waste Management Agency (Andra) in Callovo Oxfordian claystone revealed the development of a fractured zone (extensional and shear fractures) induced by the excavation. Moreover, the field monitoring during the excavation showed an anisotropic pore pressure field around the drifts with zones of marked overpressure. For drifts parallel to the horizontal major principal stress, even though the initial stress state in the drift section is quasi-isotropic, the pore pressure evolution and the mechanical response are anisotropic. These observations suggest that the intrinsic anisotropy of the material plays a key role in the response of rock formation. A poroelastic analysis of the pore pressure change induced by drift excavation is performed. The principal objective is to simulate the main trends of the pore pressure evolution with a simple model taking into account the elastic anisotropy of the material. It is shown that depending upon the permeability and the degree of anisotropy of the rock, strong overpressures can be induced by the excavation. Furthermore, it is observed that the distribution of overpressures around drifts depends also on the drifts orientation. Finally, an analysis of the onset of failure shows the key role of the hydro-mechanical coupling on the extension of the failed zone around the drifts.