Summary Elastic contrast in porous rock with fluid leads to irreversible seismic energy loss. This occurs in laminated intervals with individual layers much smaller than the seismic wavelength, even if the intrinsic attenuation in each single layer is zero. The proposed theoretical loss mechanism is macroscopic cross-flow between porous layers with differing elastic properties. A passing seismic wave creates deformation difference in this elastically heterogeneous body, hence encouraging viscous cross-flow and accompanying energy loss. Both the elastic and inelastic properties of this layered medium are anisotropic. The results indicate that the attenuation is larger in the direction perpendicular to the layers than parallel to the layers. Application of this theory to a gas hydrate well shows considerable attenuation anisotropy due to large contrast of elastic properties between hydrate-filled sand and surrounding shale.