Abstract: The sound scattering by a cylindrical interface between two different solids is briefly summarized and the transfer matrix which relates the displacement and stress across the interface is given. By asymptotically expanding the transfer matrix, one can obtain the first- and second-order boundary conditions at the interface. When the thickness of the interface layer is small compared to the cylinder radius, further simplication of the expanded transfer matrix leads to approximate boundary conditions which can be simulated by a spring model. Some numerical computations are presented to evaluate the precision of the various approximate boundary conditions. The effects of the boundary condition on sound scattering are also considered. Finally some related problems worthy to be further investigated are addressed.