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The problem of how to relate brain injury thresholds observed in animal head injury experiments to equivalent thresholds for humans is explored through study of a highly idealized model of the head. The fundamental assumption is that shear strains of sufficient magnitude cause brain injury, and that the deleterious effect of head acceleration stems from the character and severity of strain wave propagation through the brain. This paper focuses on the role of tissue mechanics in determining wave motion. The problem studied is a Maxwell-type viscoelastic cylinder subjected to a sinusoidally varying angular acceleration. The solution for the mechanical response of the cylinder yields two dimensionless groupings that fully dictate the character and severity of straining that results from this loading. Application of this model to humans is discussed.