Serious stability problems in boreholes drilled in transversely isotropic rocks have led to several studies related to the combined effect of wellbore trajectory and weakness plane inclination. The stability analyses of wellbores drilled in fields that were affected by slip along the weakness planes were carried out with software based on the weakness plane model. However, this model is discontinuous and cannot capture features of some transversely isotropic rocks. The Hoek & Brown criterion, adapted to anisotropic rocks, is a continuous criterion that can predict mud pressures in a complete range of inclination of the weakness planes. However, this criterion requires a consistent number of triaxial tests, for the determination of the controlling parameters at various inclinations of the weakness planes. Here we propose a novel procedure for the prediction of wellbore pressures in transversely isotropic rocks (typically shales) with the Hoek & Brown criterion coupled with the weakness plane model. The procedure requires a set of uniaxial compression tests performed on rock specimens at different inclinations of the weakness planes and one triaxial test carried out at an inclination of the weakness planes in the range 50°-60°. For our purposes we used the results of lab tests carried out on Opalinus clay.