Finite element modelling has been used to study the evolution of strain in a model of the human brain under impulsive acceleration loadings. A cumulative damage measure, based on the calculation of the volume fraction of the brain that has experienced a specific level of stretch, is used as a possible predictor for deformation-related brain injury. The measure is based on the maximum principal strain calculated from an objective strain tensor that is obtained by integration of the rate of deformation gradient with appropriate accounting for large rotations. This measure is used here to evaluate the relative effects of rotational and translational accelerations, in both the sagittal and coronal planes, on the development of strain damage in the brain. A new technique for the computational treatment of the brain-dura interface is suggested and used to alleviate the difficulties in the explicit representation of the cerebrospinal fluid layer existing between the two solid materials.