Abstract The porous properties of brain tissue are important for understanding normal and abnormal cerebrospinal fluid flow in the brain. In this study, a poroviscoelastic model was fitted to the stress relaxation response of white matter in unconfined compression performed under a range of low strain rates. A set of experiments was also performed on the tissue samples using a no-slip boundary condition. Results from these experiments demonstrated that the rheological response of the white matter is primarily governed by the intrinsic viscoelastic properties of the solid phase. The permeability of white matter was found to be of the order of 10 −12 m 4/Ns.