The differential equations and boundary conditions governing the macroscopic behavior of nonconducting magnetically saturated media undergoing large deformations, are derived by means of a systematic and consistent application of the laws of continuum physics to a model consisting of an electronic spin continuum coupled to a lattice continuum. The macroscopic effect of the quantum mechanical exchange interaction is included as are dissipation and the associated thermodynamics. The resulting nonlinear equations are specialized to the important case of a small dynamic field superposed on a large static biasing field. Only the linear approximation in the small-field variables is obtained. This final system of linear equations permits the solution of a variety of magnetomechanical boundary-value problems.