Techniques for solving forward and inverse wave propagation problems involving poroelastic layers will be discussed. Parabolic equation techniques are efficient for solving problems in laterally varying media. A parabolic equation for poroelastic media has been developed and applied to problems in ocean acoustics [J. Acoust. Soc. Am. 98, 1645–1656 (1995)]. This approach has been generalized to the anisotropic case. The smallness of shear speeds in many ocean sediments has motivated the study of poroacoustic media [J. Acoust. Soc. Am. 104, 783–790 (1998)], which is a limiting case of Biot theory in which the rigidity vanishes. Although parabolic equation techniques have not been fully generalized from acoustics to poroelasticity, studying the intermediate case of poroacoustics has helped to bridge the gap. The parabolic equation techniques have been used as tools for solving inverse problems. This approach is presently being applied to field data. One of the issues that arises in solving the inverse problem is the mapping between the coefficients of the wave equation and the wave speeds. The inverse of this mapping can be used to define problems in terms of natural parameters rather than moduli. [Work supported by ONR.]