Opalinus Clay shale, the selected host geomaterial of a high-level radioactive waste repository in Switzerland, was sourced at shallow depth in a borehole in the northern part of the country. Pairs of specimens, retrieved from the same depth were prepared to be tested in oedometric conditions, with loading in the direction either parallel or perpendicular to the bedding planes. The results showed a marked anisotropy of the material response in the low effective stress ranges (<10 MPa), with stiffer response in the direction of the bedding planes. The anisotropy reduced markedly at higher effective stress levels (≥10 MPa), resulting in similar compressibility in the two loading directions at the highest investigated effective stress level. Similarly, the computed hydraulic conductivity (via the consolidation theory) revealed larger differences in the low stress range, where the hydraulic conductivity is greater in the direction of the bedding planes. © Springer Nature Switzerland AG 2019.