The paper investigates the mud pressure to maintain the stability of wellbores drilled in transversely isotropic shale through sensitivity analyses, carried out with analytical and numerical modeling (FLAC). To this end, we interpreted the anisotropic strength of the Tournemire shale with the Weakness Plane Model (WPM) and the modified Hoek–Brown criterion (HBm). The sensitivity analyses of synthetic case studies indicated a different trend in mud pressure for the two criteria. In some cases, the WPM predicts mud pressures higher than those predicted by the HBm and vice versa. The mud pressures predicted by the HBm resulted in being more sensitive to the increase in the anisotropy of the far field stresses for all the inclinations of the weakness planes. In this context, the WPM predicts some anomalous low mud pressures in a wide range of inclinations of the weak planes. The change in the frictional component of strength decreases with an increase in the pore fluid pressure for both criteria. The mud pressure predicted by the WPM resulted in being more sensitive to the change in frictional strength. The change in trend of the two criteria with change in input data suggests caution in the “a priori” selection of the strength criterion. A simple solution is proposed to predict a safe and reliable mud pressure with a small number of lab tests.