Abstract: In the process of the external magnetic field falling, the high temperature superconducting (HTS) block will be affected by tensile stress, which may lead to fracture, and the crack tip will yield in a small range under the action of tensile stress. In this case, it will be inaccurate to calculate the stress intensity factor (SIF) using the linear elasticity theory. In this paper, the formula of SIF in plastic zone of crack tip is modified by the unified strength theory. Then, based on the Bean model, the influence of external magnetic field change rate and external magnetic field size on stress intensity factor is discussed respectively. The results show that when the external magnetic field decreases at a small rate, the effect of the external magnetic field on the crack growth should be mainly considered. When the external magnetic field decreases at a large rate, the effect of the external magnetic field on the crack growth should be mainly considered. The results presented in this paper have certain reference value for the calculation of crack propagation and stress intensity factor in the magnetizing process of HTS blocks.