This study considers modelling the brain due to rotation of the skull where, at lower frequencies, the shear property of the material is important. Investigations reported here cover the effect of elastic and viscoelastic (lossy) cerebral material, the effect of the Falx protruding into the brain, the gap around the Falx and the brain filled with non viscous fluid in addition to different models of the Falx with bending or membrane stiffness. Analytical benchmark formulations are also described for the simple 2D plane strain in a cylinder produced by a half-sine rotation on the outer periphery which allows numerical (Finite Element) models to be validated. The results show the importance of the material properties, duration of loading and amplitude of loading as well as the influence of the partition. The results are shown for predicted maximum Principal strains in the models, as this may well be indicative of whether damage of the brain tissue occurs.