We employ an advanced 3D computational model of the head with high anatomical fidelity, together with measured tissue properties, to assess the consequences of dynamic loading to the head in two distinct modes: head rotation and head extension. We use a subject-specific computational head model, using the material point method, built from T1 magnetic resonance images, and considering the anisotropic properties of the white matter which can predict strains in the brain under large rotational accelerations. The material model now includes the shear anisotropy of the white matter. We validate the model under head rotation and head extension motions using live human data, and advance a prior version of the model to include biofidelic falx and tentorium. We then examine the consequences of incorporating the falx and tentorium in terms of the predictions from the computational head model. © 2019, Biomedical Engineering Society.