The stress dependency of the porosity and permeability of porous rocks is described theoretically by representing the preferential flow paths in heterogeneous porous rocks by a bundle of tortuous cylindrical elastic tubes. A Lame-type equation is applied to relate the radial displacement of the internal wall of the cylindrical elastic tubes and the porosity to the variation of the pore fluid pressure. The variation of the permeability of porous rocks by effective stress is determined by incorporating the radial displacement of the internal wall of the cylindrical elastic tubes into the Kozeny-Carman relationship. The fully analytical solutions of the mechanistic elastic pore-shell model developed by combining the Lame and Kozeny-Carman equations are shown to lead to very accurate correlations of the stress dependency of both the porosity and the permeability of porous rocks.