Shale gas well deliverability and economics depend on extremely low permeability that is not only dependent on the rock bedding trend but also controlled by in situ stresses. The purpose of this study was to determine relative contributions of normal and tangential stresses with respect to the rock bedding plane on permeability evolution of shale. The study involved an analysis of the rock bedding structure, followed by triaxial testing of rock samples and theoretical modeling. Also simulated were the effects of stress-bedding and load cycling. The results showed shale permeability reduction during the stress loading process and its gradual recovery during the unloading process. Permeability change was more pronounced in response to normal stress but some effects of the tangential stresses were also observed. Moreover, a theoretical model was derived to describe permeability change with effective stress in the presence of normal and tangential stresses. The model was empirically matched with the experimental results. The assessment of relative contributions of normal and tangential stresses was quantified with the analysis of variance (ANOVA). The analysis revealed significance levels of normal stress, and two tangential stresses σt1 and σt2 on shale permeability as 81%, 5%, and 14%, respectively. An almost 20-percent contribution of tangential stress loading to permeability response indicates a need for the improvement in computing effective stress. Therefore, a new method was suggested to determine effective stress when predicting permeability evolution of shale.