Blast-induced neurotrauma has become an increasing concern with the advancement of explosive devices and high rates of loading. Recent experiments show that under blast loading conditions, brain tissue undergoes small displacements that are much lower than the threshold of traumatic brain injury. Based on the nonlinear viscoelastic nature of brain tissue, stress waves generated in the tissue due to blast loading can evolve into shock waves, which create high spatial and temporal pressure gradients at the shock front. In this study, the effect and importance of shock front thickness in simulating the response of tissues in shock tube scenarios has been investigated. It is shown that such measures can have a significant effect on prediction on injury in computational models.