Abstract: To understand the characteristics of hydraulic fracture initiation and optimize the design and treatment of hydraulic fracturing,the maximum tangential stress criterion is used to predict hydraulic fracture initiation. The equation of initiation angle and critical initiation pressure is derived. The variations of initiation angle/critical initiation pressure under the influence of prefabricated crack inclination angle,hydraulic pressure,stress difference,and pore pressure are analyzed. The results show that the initiation angle rises first and then declines with the inclination angle increment. With the rise of hydraulic pressure,the initiation angle declines progressively. The initiation angle rises monotonically with the stress difference. The initiation angle falls monotonously with the rise of pore pressure. The critical initiation pressure rises monotonously with the increment of the crack angle. In general,the critical initiation pressure rises with the increment of stress difference. The critical initiation pressure declines with the increment of crack length. The critical initiation pressure rises monotonously with the fracture toughness. The critical initiation pressure drops monotonously with the rise of pore pressure. It is found that the initiation angle and critical initiation pressure predicted by the maximum tangential stress criterion are in good agreement with the experimental result. The research provides some references for the design and treatment of hydraulic fracturing.