White matter in the brain is thought to be mechanically anisotropic and vulnerable to mechanical strain. By studying mechanical shear wave propagation in ex vivo brain tissue using magnetic resonance elastography (MRE), and comparing to results from computer models, shear moduli and shear anisotropy were estimated. This method allows the relaxation of assumptions of isotropy and homogeneity in traditional MRE inversions. The ratio of shear moduli governing shear parallel and perpendicular to fiber direction was approximately 1.25, indicating mild anisotropy in shear. This quantitative characterization of shear anisotropy in white matter has important implications for traumatic brain injury modeling.