Brain injury has been researched since the 1940s and various methodologies have been discussed for evaluating brain injury risk in vehicle crash tests. In recent years, an angular velocity based brain injury criterion (BrIC) has been proposed by the National Highway Traffic Safety Administration (NHTSA) for use in regulatory or consumer vehicle safety assessment tests. One of the brain injury mechanisms can be explained by relative displacement between the brain and skull, resulting in brain deformation and strain. This paper states a hypothesis of this brain injury mechanism using a simple mass-spring-damper model. Then the hypothesis was verified by the Simulated Injury Monitor (SIMon) version 4.0, a finite element model of the human head developed by NHTSA, using a cumulative strain damage measure (CSDM) as the brain injury metric. In consequence, CSDM varies according to the input loadings, which have the same peak angular velocity but different levels of peak angular acceleration and loading durations. These results suggest that in order to evaluate brain injury risk accurately, an angular velocity based criterion may not always be sufficient and it may be necessary to consider the peak value of angular acceleration and the corresponding loading duration. This hypothesis was applied to NHSTA’s research test data to prove its validity. It was found that brain injury risk predicted by CSDM can be comparatively lower than that predicted by BrIC and vice versa.