Abstract: Hydraulic fracturing (HF) has achieved significant commercial success in unconventional oil and gas development. However, it has the potential to induce fault slip. This study investigates the physical mechanisms underlying potential fault slip triggered by HF operations under varying geological and operational constraints. First, we elucidate the relationship between the critical stress state and the elastic modulus of the fault, and refine a formula for the maximum crustal stress difference on critically stressed faults, including stress concentration, friction, and dip. Second, we compare the role of injected fluid in permeable faults with that in impermeable faults, and demonstrates that fault slips can be triggered by a combination of friction decrease and pore pressure increase, even after ceasing injection. Specifically, we reveal that friction decline dominates induced fault slip on high permeable and hydraulically connected fault. Third, based on experimental results and theoretical analysis, we quantify the influence region of stress transfer under different conditions of well location and injection pressure. The results reveal that the elastic modulus of the fault control the stress concentration on the fault plane. The dip of the fault and the stress concentration jointly determine the maximum crustal stress difference required for failure in critically stressed reverse faults. Thus, our study is more accurate in estimating the proximity of the in-situ stress to the critical state, compared with traditional methods. For critical reverse faults, the risk of induced slip is positively correlated with both injection pressure and friction of fault plane. When the injection pressure (PI) is 100 MPa and the friction (μ) is 0.8, the safe distance from injection point to critically stressed faults along the direction of maximum principal stress and maximum principal stress (dH and dv) should exceed 25 and 18 times as the hydraulic fracture half-length. When PI is 100 MPa and μ is 0.6, dH and dv are 23 and 17 times as the hydraulic fracture half-length, respectively. When PI is 60 MPa and μ is 0.6, dH and dv are 18 and 13 times as the hydraulic fracture half-length, respectively. The works enhance our understanding of HF-induced fault slip and potentially guide designs of the shale gas well location and trajectory for safer production.