Abstract: In the paper, the analytical solution for interfacepoints in a short time window is firstly deduced by combination of thefiniteness of wave velocity and solutions of Cauchy problem of waveequation, then a method of constructing a high order explicit recursionformula for interface points is provided for numerical simulation of scalarwave motion in uniformly layered model. To illustrate the main point, anexample of constructing recursion formula for interface points presented ina piecewise elastic bar is included. Second and fourth order recursionformula for interface in time and space are provided and consistent with thecurrent stable explicit formulas for interior points. Like heterogeneousscheme, the scheme presented in this paper has the same advantage of easyprogramming. Finally, the accuracy and stability of the new scheme arevalidated through numerical tests.