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The scientific work considers the finite element modeling of fluid filtration in a deformable porous medium. A transversely isotropic medium has been taken as a deformable medium. Fluid filtration process to horizontal wells by drift type direction occurred in this transversely isotropic medium is studied. As filtration process goes, the stress layers are associated with the pressure, accordingly, equations have been shown regarding to this pressure. Numerical solution of the problem is carried out using the finite element modeling.