Stress dependency of permeability of porous rocks is described by means of a theoretical elastic cylindrical pore-shell model. This model is developed based on a bundle of elastic capillary tubes representation of the preferential flow paths formed in heterogeneous porous rocks. The radial displacement caused in tubes by the pore fluid pressure applied over the surface of the elastic cylindrical flow tubes is expressed by a Lame-type equation. The radial displacement is incorporated into the Kozeny-Carman relationship to determine the variation of the permeability of porous rocks by variation of the pore fluid pressure. The solution of this equation yields a semi-analytical equation which provides accurate correlations of the stress dependency of the permeability data of porous rocks. The errors associated with the previous formulation of this problem by Zhu et al. (Transp Porous Med 122:235-252, 2018) are explained in view of the present formulation.