Magnetic resonance elastography (MRE) is an MRI technique for imaging the mechanical properties of brain in vivo, and has shown differences in properties between neuroanatomical regions and sensitivity to aging, neurological disorders, and normal brain function. Past MRE studies investigating these properties have typically assumed the brain is mechanically isotropic, though the aligned fibers of white matter suggest an anisotropic material model should be considered for more accurate parameter estimation. Here we used a transversely isotropic, nonlinear inversion algorithm (TI-NLI) and multi-excitation MRE to estimate the anisotropic material parameters of individual white matter tracts in healthy young adults. We found significant differences between individual tracts for three recovered anisotropic parameters: substrate shear stiffness, μ (range: 2.57 – 3.02 kPa), shear anisotropy, φ (range: -0.026 – 0.164), and tensile anisotropy, ζ (range: 0.559 – 1.049). Additionally, we demonstrated the repeatability of these parameter estimates in terms of lower variability of repeated measures in a single subject relative to variability in our sample population. Further, we observed significant differences in anisotropic mechanical properties between segments of the corpus callosum (genu, body, and splenium), which is expected based on differences in axonal microstructure. This study shows the ability of MRE with TI-NLI to estimate anisotropic mechanical properties of white matter and presents reference properties for tracts throughout the healthy brain. Statement of significanceIn this study we use magnetic resonance elastography to determine the mechanical properties of white matter, which can be useful in characterizing neurological conditions such as multiple sclerosis and traumatic brain injury. However, due to its fibrous nature, accurate estimation of mechanical properties of white matter requires an anisotropic material model. In this work, we use a transversely isotropic inversion algorithm with data from multi-excitation MRE to determine the anisotropic mechanical properties of white matter in a healthy young population based upon an anisotropic material model. We display the ability of MRE to capture structural differences between different white matter tracts and sub-regions of these tracts, which are expected to reflect differences such as average axon thickness and myelin density. This robust estimation of white matter anisotropic properties in a young, healthy population provides an avenue for future studies to implement these methods to examine brain development, aging, and pathology.