The confining pressure imposed on a shale formation has a significant impact on the apparent permeability of the rock. Gas flow in low-permeability shales differs significantly from liquid flow because of the Klinkenberg effect, which results from gas molecule slip at the wall surfaces inside the nanopores. This effect causes the increase of apparent permeability (i.e., the measured permeability). In this study, cores extracted from four U.S. shale formations were tested using a pulse decay permeameter (PDP) under varying combinations of confining and pore pressures. The Klinkenberg coefficient was calculated to interpret the change in the measured apparent permeability as a function of pore pressure and effective stress. Next, based on the various combinations of confining and pore pressures, the actual values of the Biot coefficient were calculated by data fitting. Moreover, the samples were cored in the directions parallel to and perpendicular to the shale bedding planes to unravel the role of bedding plane direction on the apparent permeability. Furthermore, a novel, multi-physics shale transport (MPST) model was developed to account for the coupled multi-physics processes of geomechanics, fluid dynamics, and Klinkenberg effect for gas transport in shales. In the MPST model, pore pressure and effective stress are the two independent input variables, and the measured apparent permeability is the model output. The MPST model was then used to fit the PDP experimental data, and the successful data fitting confirmed that the MPST model captures the critical multi-physics processes that regulate the apparent permeability.