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This study explores the application of viscoelastic modeling for characterization of the response of the brain to impulsive loading with the objective of learning whether such models could exhibit the same time dependency of strain or likelihood of injury, as exhibited by the Severity Index, HIC Index, Wayne Tolerance Curve, and other similar representations of tolerance. The mathematical relationships between viscoelastic properties and the corresponding time dependency of tolerance are shown for Newtonian, Bingham plastic, and Pseudo-Bingham, as well as more general behavior. Preliminary static and dynamic tests upon small mammalian material are described with particular attention given to strain in the vicinity of the brainstem as a function of loading profile. Both the theoretical and experimental results show that the falling time dependency of the above indexes can be interpreted in terms of nonlinear viscoelastic response.