This chapter starts by providing the background physics covering reference system and coordinate system, angular velocity and its combination, generalization of Newton’s second law of motion into a translating and rotating reference system, gravity and gravity potential, Lagrangian and Eulerian descriptions of position and velocity of a continuum, dynamic equations of motion of a continuum, deformation of a continuum, and elasticity. Particular care is taken for the formulation to be general enough for studying the dynamics of the earth. The separation of the general motion of the Earth into three components—translation, rotation and deformation—is rigorously formulated. The equations derived include the equation of the translational motion of the center of mass, the equation of rotation of the Tisserand frame around the center of mass, and the elastic deformation with respect to the Tisserand frame. The elastic deformation of the translating and rotating prestressed general Earth model is formulated in extreme detail, most notably, the derivation of the constitutive equation and the boundary conditions. The hydrostatic equilibrium state considered as the undeformed configuration, which is mostly the case in the literature, is treated as a degenerate instance.