This study investigates the propagation of shock waves and self-preserving waves in soft tissues such as brain as a mechanism of injury in high rate loading conditions as seen in blastinduced neurotrauma (BINT). The derived mathematical models indicate that whereas linear viscoelastic models predict only decaying waves, instances of such phenomena as shock can be achieved in nonlinear media. In this study, a nonlinear viscoelastic material model for brain tissue was developed in compression. Furthermore, nonlinear viscoelastic wave propagation in brain tissue was studied and a criterion for the development of shock waves was formulated. It was shown that discontinuities in the acceleration that happen in blast loading conditions may evolve to shock waves, resulting in large discontinuities in strain and stress at the wave front leading to tissue injuries. Copyright c 2011 by ASME.