Theory of inelastic electron tunneling spectroscopy (IETS) of single adsorbates on metal surfaces with scanning tunneling microscope (STM-IETS) is presented. Adsorbate induced resonance model for studying tunneling processes via vibrational excitation of adsorbates enables us to derive general formulae for the elastic and inelastic tunneling currents. The condition under which the IETS spectrum (d²I/dV²) directly reflects the vibrational density of states of adsorbates was determined. It is found that two different time scales associated with the lifetime of tunneling electrons in the adsorbate and the residence time of electrons due to shuttling between the substrate/tip and adsorbate playimportant roles in the various features of STM-IETS spectra, including peak, dip, derivative-like or asymmetric structures.