This chapter discusses vibrational properties and excitational properties of surfaces phonons. The field of surface phonons has had an enormous upsurge in interest during the past decade arising from important experimental and theoretical developments. On the experimental side, improvements in the techniques of inelastic helium atom scattering and inelastic electron scattering have made possible the experimental determination of surface phonon dispersion curves for surfaces of metals, semiconductors and insulators. Valuable information concerning the forces of interaction between atoms at and near the surface of a crystal has been obtained for both clean surfaces and surfaces with adsorbed atomic and molecular species. On the theoretical side, the possibility of making first-principles calculations of the force constants characterizing the interactions of a surface atom with neighboring atoms has come much closer to reality as a result of the development of supercomputers. This chapter also discusses the surface acoustic wave in isotropic media. In the limit that the wavelength of a vibrational wave is large compared to the interatomic spacing of the crystals, elastic continuum theory (ECT) can be used to investigate surface vibrational waves. This procedure was employed by Lord Rayleigh who studied an isotropic elastic continuum with a planar stress-free surface. The displacement vector for a Rayleigh wave lies in the sagittal plane defined by the normal to the surface and the direction of propagation.