Borehole Breakouts in Transversely Isotropic Posidonia Shale Borehole instabilities are frequently encountered when drilling through finely laminated organic rich shales (Økland and Cook 1998; Ottesen 2010; etc.); such instabilities should be avoided to assure a successful exploitation and safe production of the contained unconventional hydrocarbons. Borehole instabilities such as borehole breakouts or drilling induced tensile fractures may lead to poor cementing of the borehole annulus difficulties with recording and interpretation of geophysical logs low directional control and in the worst case the loss of the well. If these problems are not recognized and expertly remedied pollution of the groundwater or the emission of gases into the atmosphere can occur since the migration paths of the hydrocarbons in the subsurface are not yet fully understood (e.g. Davies et al. 2014; Zoback et al. 2010). In addition it is often mentioned that the drilling problems encountered and the resulting downtimes of the wellbore system in finely laminated shales significantly increase drilling costs…