The Head Injury Criterion (HIC) has been employed as a measure of traumatic brain injury arising from an impact involving linear acceleration. Some investigators have been reported the shortcomings of the HIC regarding the angular accelerations, head mass and the precise threshold of injury level [1, 2]. In this study the effect of acceleration curves, as a frontal impact, and the HIC values on the strain in the brain was critically analyzed. Specifically in this paper, the strains in the brain for three sets of acceleration pulses, where the peak of the curve takes place early or later (advanced or delayed) during the pulse time, were investigated. The results of this study indicate that for two different acceleration pulses, with the same peak value, duration and the same HIC values the strains in the brain are different. Therefore there is a need for further research leading to better criteria or modification of the HIC as it relates to the Traumatic Brain Injury (TBI).