For many years many efforts have been performed in the laboratory experiments to duplicate the reservoir conditions. In this study, we will investigate the permeability change at different overburden conditions. The reduction in permeability with overburden pressure has been well known. Fatt and Davis (1952) presented the changes in permeability with pressure at range 0 to 15,000 psig and found that overburden pressure caused a reduction in permeability of the consolidated oil-bearing sandstone samples by as much as 50% at 10,000 psig. Wyble (1958) performed similar experiments on three different sandstone samples to determine the changes in conductivity, porosity and permeability at pressure range 0 to 5,000 psig. His results were consistent with the observation by Fatt and Davis (1952). During the experiments, different overburden pressures (radial force) were applied only to the cylinder core while the axial direction was kept at constant atmospheric pressure. Gray et al. (1963) enhanced the previous experiments by applying axial force and combining with overburden pressure (radial force) to measure the anisotropy permeability changes at more representative reservoir stress-state condition. They showed that permeability reduction subjected to overburden pressure as a function of the ratio of radial to axial stress and the permeability reduction …