In a layered system, the interface between two media presents an intrinsic inhomogeneity even when the materials are isotropic and homogeneous in the sense of continuum medium description of wave propagation. In terms of the rigid bonding (RB) model, the material parameters behave as piecewise continuous functions with an abrupt change across the interface. Therefore, it is reasonable to expect that the wave experiences a singular potential at the border formed by the space derivatives of the material parameters. However, we prove that this potential is strictly cancelled due to continuity of the stress field. The equations governing acoustic wave propagation are derived by the partial wave decomposition method.