The basic elements of a mathematical analysis of a three-dimensional vehicle (cockpit)-occupant simulation model are presented. The model employs Hanavan's finite segment human body model and possesses 31 degrees of freedom. The dynamical analysis is based upon Lagrange's form of d'Alembert's principle, which systematically provides for an efficient computer-oriented derivation of the governing dynamical equations of motion. The model possesses a broad range of application. An elementary study of a front-end collision is presented as an illustrative example.