Diffusion through a multilayered material is analysed by means of the Laplace transformation. An algorithm using a new method for numerical inversion of the Laplace transform is successfully developed for solving the diffusion equations. The procedure is applied to an analysis of hydrogen permeation through a simple multilayered material related to electrochemical testing. The problem appears simple, but the exact analytical solution is difficult; the present technique makes it possible to solve this problem while retaining a part of the advantage of the analytical method. The results are compared with results obtained by the conventional analytical method, which is based on diffusion through a single layer. The applicability and limit of use of the conventional analytical method is also investigated.