Abstract The successful exploitation of geothermal reservoirs relies upon the understanding of fluid circulation in the subsurface. However, large-scale fluid flow modelling often assumes that the permeability of the layers of rock within the model are isotropic. We present here a laboratory study in which we assessed the permeability anisotropy of seven Buntsandstein sandstone cores taken from the geothermal reservoir at Soultz-sous-Forêts (France) in the Upper Rhine Graben. The porosity and permeability of our samples, cored parallel and perpendicular to bedding, ranged from 5.2 to 16.3% and from 2.48 × 10 −18 to 7.66 × 10 −14 m 2 , respectively. Our data show that permeability anisotropy can be up to four orders of magnitude in sandstones from the Buntsandstein, and that permeability anisotropy increases as a function of increasing porosity. Quantitative microstructural analysis combined with permeability modelling shows that the permeability anisotropy is the result of fine-grained and low-permeability laminations that are parallel or sub-parallel to bedding. We suggest, based on our data, that permeability anisotropy should be considered in future fluid flow modelling at geothermal sites within the Upper Rhine Graben.