This chapter begins with coverage of the quantitative concepts used to describe the deformation of solids by seismic waves, namely the concepts of stress, strain, and dilatation. This is followed by the derivation of equations for describing seismic wave motion in the subsurface, namely, the equation of motion, conservation of energy, kinetic and strain-energy density, intensity or energy flux, the stress–strain relation, isotropy, hydrostatic stress, elastic constants (which are related to the nature of the medium in which waves travel), the wave equations, compressional and shear waves, plane harmonic waves, displacement potentials, Helmholtz equations, near-field and far-field waves, mean values, and the acoustic wave equation. The chapter ends with examples that discuss seismic waves produced by a buried explosive charge and by a directed point force, and discussions of the moment tensor and apparent velocities.