Elastic properties of finely layered media are of great interest for seismic exploration. Theoretical models give a dependence of overall properties on constituent parameters. On the one hand they help geophysicists to estimate possible ranges of anisotropy and on the other hand they provide a basis for interpretation of measured anisotropic parameters in terms of microstructure. Last forty years such models with elastic constituents have been extensively used. Recently they have been updated for describing fractured rocks (Hsu and Schoenberg, 1993). in this case thin. and soft elastic layer models fracture. However reservoir rocks are porous and permeable. Porosity and permeability are taken into account by well-known Blot model. Finely layered porous sequences have some distinctive properties which are the topic of modern research (Schoenberg, 1996). Therefore it is important to update developed concepts to porous medium. Bakulin and Molotkov (1998, 1997) who generalized Backus averaging on poroelastic medium have done first step. Here we pay attention to one special case when there is only one preferential direction of fluid flow in porous rock. This may be caused by presence of impermeable barriers or lenses, which are modeled as set of solid layers intersecting porous medium. Such model corresponds to highly hydraulically anisotropic rock, which has very strong anisotropy of pore space structure and permeability.