Hydrocephalus is a cerebral disease where brain ventricles enlarge and compress the brain parenchyma towards the skull leading to symptoms like dementia, walking disorder and incontinence. The origin of normal pressure hydrocephalus is still obscure. In order to study this disease, a finite element model is built using the geometries of the ventricles and the skull measured by magnetic resonance imaging. The brain parenchyma is modelled as a porous medium fully saturated with cerebrospinal fluid (CSF) using Biot’s theory of consolidation (1941). Owing to the existence of bundles of axons, the brain parenchyma shows locally anisotropic behaviour. Indeed, permeability is higher along the fibre tracts in the white matter region. In contrast, grey matter is isotropic. Diffusion tensor imaging is used to establish the local CSF content and the fibre tracts direction together with the associated local frame where the permeability coefficients are given by dedicated formulas. The present study shows that both inhomogeneous CSF content and anisotropy in permeability have a great influence on the CSF flow pattern through the parenchyma under an imposed pressure gradient between the ventricles and the subarachnoid spaces.