This thesis is a study of acoustic wave propagation in fluid, elastic and poro-elastic media in general and it is a study of underwater acoustics with an interacting seabed in specific. In the first chapter we transform the equations describing acoustic wave propagation in a fluid, elastic, and poro-elastic medium to implement the Thompson-Haskell technique in solving the boundary-transmission problem. The Hankel transform of the equations of elasticity and poro-elasticity is a generalization of the work of Ahluwalia and Keller in fluid acoustics. The fundamental properties of the Biot equations are investigated and new results are proved. These results are essential starting points for potential theory of poro-elasticity. The Biot operator is shown to be elliptic in the sense of Douglas and Nirenberg; moreover, we calculate the fundamental solution to the Biot equations of acoustics. In the last chapter, we investigate the problem using the method of singular perturbations to calculate an approximate Green's function for the combined ocean-seabed system.