In the framework of a deep geological radioactive waste disposal in France, the hydromechanical properties of the designated host rock, the Callovo-Oxfordian claystone (COx), are investigated in laboratory tests. Experiments presented in this study are carried out to determine several coefficients required within a transversely isotropic material model. They include isotropic compression tests, pore pressure tests, and deviatoric loading tests parallel and perpendicular to the bedding plane. We emphasize the adapted experimental devices and testing procedures, necessary to detect small strains under high pressures, on a material, which is sensitive to water and has a very low permeability. In particular, we discovered a significant decrease of elastic stiffness with decreasing effective stress, which was observed to be reversible. In both isotropic and deviatoric tests, a notable anisotropic strain response was found. The Young modulus parallel to bedding was about 1.8 times higher than the one perpendicular to the bedding plane. A notably low Poisson ratio perpendicular to the bedding plane with values between 0.1 and 0.2 was evidenced. While the anisotropy of the back-calculated Biot coefficient was found to be low, a significant anisotropy of the Skempton’s coefficient was computed. The performed experiments provide an overdetermined set of material parameters at different stress levels. Using all determined parameters in a least square error regression scheme, seven independent elastic coefficients and their effective stress dependency are characterized. Parameters measured under isotropic loading are well represented by this set of coefficients, while the poroelastic framework with isotropic stress dependency is not sufficient to describe laboratory findings from triaxial loading.