Abstract: A spring model for simulating the interface between two solids is presented. The model was proposed initially on the basis of elastic deformation of an interface under externally applied forces, then later modified by asymptotically expanding the transfer matrix for an interfacial thin layer from which acoustic wave reflection is involved. The general boundary conditions at an interface are obtained, which depend on the stiffness constants and masses of the interface springs. Explicit expressions for the acoustic reflection coefficients from the interfaces are given and ultrasonic experiments for measuring the interface stiffness constants are described. Finally, some discussion is given of current research on interactions between sound waves and interfaces.