Abstract: Based on Biot’s theory, a series solution for the scattering of an elastic wave by a cylindrical shell in a homogeneous saturated half-space was investigated theoretically with the assumption that the shell material was also a saturated medium. The wave potentials were expanded in Fourier-Bessel series using the wave function expansion method. A convex approximation was used to replace the straight boundary of the half-space. In terms of continuity conditions and boundary conditions of the problem, the unknown coefficients in potentials were determined. Numerical results show that radial stress amplitudes at the interface of the saturated soil and shell depend on the relative permeability of the saturated soil and shell and the angle of incidence. The radial stress amplitudes are significantly affected at the interface of the shell bed and soil when the relative permeability is low.