The observation of surface phonon dispersion using local probes can provide important information related to local structural and thermal properties. In this study, surface phonon modes on a Cu(100) surface were measured using the inelastic tunneling spectroscopy of scanning tunneling microscopy (STM-IETS) with atomically sharp tips. Different phonon modes were selectively measured depending on the structures of the probing tips or the surfaces. Two different surface phonon modes, at 19.0 meV on a clean Cu(100) surface and at 13.5 meV on an oxygen-adsorbed Cu(100) surface, are explained by the selection rules. Additionally, the spatial variation in STM-IETS showed surface stress relaxation.