The determination of the transversely isotropic poroelastic parameters and the permeability of the Opalinus Clay, a possible host rock for deep radioactive waste disposal in Switzerland, is necessary for better predicting the hydromechanical response around the galleries. Transient experiments with fast undrained loading followed by a drainage phase, established for testing very low permeability claystones like the Opalinus Clay, were carried out on a sample equipped with strain gauges. The data obtained with this procedure showed that the values of a given poroelastic parameter, obtained from different loading paths, are reasonably close to each other, indicating that measurements are reliable and repeatable. An average intrinsic permeability perpendicular to bedding of 1.68 × 10$^{–21}$ m$^2$ was back-calculated through two consolidation phases, with similar values after loading and unloading. Some parameters, such as drained and undrained bulk moduli, exhibit a strong anisotropy. Conversely, some other parameters, like the Biot coefficients parallel and perpendicular to bedding, are close to each other. The values of these parameters were compared with those from other studies, enlarging the existing database of the hydromechanical properties of Opalinus Clay.