Inelastic electron tunneling spectroscopy (IETS) combined with scanning tunneling microscopy (STM) allows us to acquire vibrational signals at surfaces. In STM-IETS, a tunneling electron from the STM tip excites vibrations whenever the energy of the tunneling electron exceeds the vibrational energies. This opens up an inelastic channel in parallel with the elastic one and gives rise to an increase/decrease of the conductivity. As a consequence, a pair of peak and dip shows up at the bias voltages with respect to the Fermi level corresponding to the energy of vibrational energy. Until recently, the application of STM-IETS was limited to the localized vibration of single atoms and molecules adsorbed on surfaces. In principle, STM-IETS should be capable of detecting collective lattice dynamics, i.e., phonons. In this paper, I will introduce the theory of STM-IETS measurement for a metal surface and the application of this theory for surface phonons on Cu(110).