We had obtained the semiempirical functions for describing the interaction properties in the ground state of Cu by using the Embedded Atom Method (EAM). In this work, The formula of surface Yorce constants between planes are derived, the force constants between planes of Cu (100), (111) and (110) surfaces are then calculated, which show that the EAM can distinguish the difference of interatomic interactions in the bulk and near the surface, and distinguish the difference of interatomic interactions near different structural surfaces. The calculated force constants lead to good agreement between the projected state densities of surface vibrations calculated by Recursion Method and the experimental results of electron-energy-loss-spectroscopy.