Abstract: Hydraulic fracturing is a promising technique used in oil and gas reservoirs, enhanced geothermal systems, and coal gas production.Although its use is widespread, many aspects of hydraulic fracturing are still not well understood and need to be further investigated to achieve increases in oil and gas production while mitigating the adverse aspects of hydraulic fracturing.Understanding how hydraulic pressure extends preexisting fractures and forms a complex fracture network is essential for the design and treatment of hydraulic fracturing.Critical water pressure and fracture initiation angle are two important parameters involved in the hydraulic fracture propagation process and production from a well.In the present study, a minimum strain energy density criterion, which considers the effects of T-stress and Poisson's ratio, was proposed to analyze fracture initiation during hydraulic fracturing.The fracture initiation angle for different crack types was investigated using the proposed theoretical method, and the results indicate that the fracture initiation angle is not only related to the stress intensity factor but also affected by the T-stress and Poisson's ratio.The critical water pressure and critical initiation angle for two symmetric radial cracks emanating from a pressurized borehole were investigated, and the theoretical results were consistent with the experimental results.Through the proposed theoretical method, the influence of T-stress, radius of the fracture process zone, Biot's coefficient, lateral pressure coefficient and Poisson's ratio on the hydraulic fracturing behavior was analyzed.Parameter analysis indicates that the radius of the fracture process zone, T-stress, and lateral pressure coefficient play an important role in the critical initiation angle and critical water pressure.The critical water pressure increases with the decrement of Poisson's ratio, whereas the critical initiation angle shows the opposite trend.Biot's coefficient has no effect on the critical initiation angle but has a significant influence on the fracture initiation angle under high water pressure.The theoretical model enables a comprehensive understanding of the characteristics of hydraulic fracturing under complex loading conditions.The results also provided a basis for quantitative investigations of the engineering design of hydraulic fracturing treatments.