The present article deals with the study of phase velocities of elastic waves in the medium of swelling porous. The medium consist of mixtures of solid, fluid and gas. Based on Eringen's linear theory of swelling porous, it is found that the existence of three longitudinal waves and two transverse waves, propagating with distinct velocities which are attenuated. Discussions of the particular cases are presented. Numerical and analytical calculations of phase velocities and attenuation are depicted graphically.