An isotropic elastic porous structure whose initial geometry is regular (periodically uniform) will experience non-uniform deformation when a viscous fluid flows through the matrix under the influence of an externally applied pressure difference. In such a case, the flow field will experience a non uniform pressure gradient whose magnitude increases in the direction of bulk flow. The closed solution to the problem of low Re flow through deformable porous media requires the simultaneous solution of the flow field in the void space and of the stress distribution in the solid matrix. The focus of the current study is to attempt to predict the pressure distribution of the flow field based only on the geometry of the media. The intention is to eventually simplify the coupled fluid-solid problem by replacing explicitly solution of the flow field with a pressure boundary condition in the stress distribution of the solid matrix.