This chapter briefly considers the governing equations for the motion of solids, and some examples of their solution. The key concepts in the dynamics of deformable solids are continuity, compatibility, and the relevant constitutive law. The chapter discusses continuum mechanics in the context of these three C’s. It briefly defines each of them. Continuity signifies that density is a definable, continuous function. Compatibility implies that all displacements must be continuous. A Constitutive law relates deformation (strain) to loading (stress). If a material is a “continuum,” we can ignore the fundamentally discrete composition of matter and to assume that the substance of material bodies is continuously distributed. The stress tensor for a given body reflects its response to all external loads, and so, by writing the stress tensor we have effectively written the resultant surface force on the body.