Abstract Void space and permeability are two primary factors controlling the movement and storage of fluids in rock and sediments. To investigate fluid flow anisotropy in Berea sandstone, permeability was measured in three perpendicular directions under effective confining pressure as a function of pore pressure. Permeability anisotropy was observed slightly in the normal and in two parallel directions to the bedding planes. We introduced microfocus X-ray computed tomography (CT) as a non-destructive tool and the three-dimensional medial axis (3DMA) method to quantify the flow-relevant geometric properties of the voids structure. Using this apparatus and structure analysis software, we obtained the distributions of pore size, throat size and the number of connecting paths between two faces in an arbitrary region of Berea sandstone. Using these data, we also evaluated the number of connecting paths between two faces and tortuosity within an arbitrary region, and discussed the relationship between permeability anisotropy and voids geometry.