A model is proposed to study atomic displacements at interfaces of multilayer structures. The theory takes into account the discrete nature of the lattice, the characteristics of the phonon spectrum (Born-von Karman Matrix), the profile of the multilayer structure, and the ability of a solute atom to distort the host lattice (Kanzaki forces). Application of the model on Au-Ni nanoscale multilayers shows large inhomogeneous displacements near the interfaces and the existence of interface interference relaxation phenomena.