Since traditional hydraulic fracturing initiation models are primarily based on linear elastic theory, they are not applicable for the elastoplastic reservoirs. Therefore, it is necessary to explore a new initiation model on the basis of the nonlinear constitutive equation. Considering the total deformation theory of plasticity, a model is established for the stress field around a well. Furthermore, an elastoplastic hydraulic fracturing initiation model is proposed according to the stress distribution model and failure criteria of elastoplastic rock. The results show that once the rock is yielded, the effect of stress concentration around the wellbore is greatly weakened and the circumferential tensile stress decreases and even disappears. The initiation pressure is higher than that predicted by the linear-elastic theory. There are two types of fracturing initiation modes including tensile and shear failures, and the shear failure is characterized by a failure angle. When the hardening index of rock is not greater than 0.5, only shear failure takes place. However, when the hardening index is greater than 0.5, the shear failure tends to happen more frequently when the values of yield stress, hardening index, internal friction angle and cohesion are small; on the contrary the tensile failure occurs.