The present paper deals with the axial symmetric cylindrical waves propagating through a cylindrical bore in swelling porous elastic medium. The secular equations, connecting the phase velocity with wave number, radius of bore and other parameters for empty and liquid filled bore are derived. A particular case of interest has also been deduced. Numerical computations have been performed and have also been shown graphically to understand behavior of phase velocity and attenuation coefficient in swelling porous (SP) and elastic medium (EL).