The equations of motion for anisotropic poroelastic inhomogeneous media admit separable SH wave motion for the case of azimuthal isotropy coupled with coaxial inhomogeneity and poroelasticity with a diagonal permeability tensor. In homogeneous examples of such media, the low-frequency waves exhibit differential attenuation that is more pronounced along the symmetry axis. If this differential attenuation can be observed, it may be used to deter-mine the permeability of the medium. Media with a vertical gradient of both elastic and permeability proper-ties show different effects. For low-frequency waves, the attenuation acts so as to reverse the effects of elastic parameter gradients on SH wave amplitudes.