This paper describes a mathematical model for head injury prediction based on the hypothesis that injury results from a combination of displacement and rotation of the brain inside the skull.

The model is a 12-degrees-of-freedom mechanical system consisting of masses, dashpots, and springs. The classical Lagrange's method is used informulating the equations of motion. Numerical integration is used to obtain their solution.

Constants for the elements of the model are obtained from published experimental measurements. Other lumped parameters which have not yet been measured are determined by adjusting them until a satisfactory agreement is obtained between the model's response and equivalent measured responses.

The frequency and time responses of the model, for a variety of loading conditions, are studied. Results show a good agreement between experimentally observed and mathematically generated responses. Quantitative validation of some responses was prevented for the lack of experimental measurements. Nevertheless, the model provides a way of using multiple injury criteria to estimate the injury potential of severe impact environments.