The mechanical performance of solid oxide fuel cell is one of the main factors limiting its commercialization process. In order to reduce the degree of crack propagation during the cooling process and improve the stability and durability of the cell, the finite element analysis is conducted on a three-dimensional model of solid oxide fuel cell containing pre-cracks. Utilizing the extended finite element method (XFEM) and fracture theory, considering the stress distribution, length and maximum width after crack propagation and deflection angle of crack as criteria, this paper investigates the influence of various parameters, including working temperature, material properties, pre-crack angle and pre-crack location, on pre-crack propagation behavior and proposes a solution to improve the stability of the cell based on material optimization and structural optimization. Set a pre-crack at the left boundary of the anode to analyze the influence of different operating conditions on the propagation of anode cracks in the cell. The correctness of finite element simulation is verified by comparing the simulation results and theoretical results of crack stress intensity factors in the same model. From the comprehensive analysis of the thermal stress of the cell, the crack length and maximum width after pre-crack propagation, and the two deflection angles of crack propagation, it can be seen that within the selected parameters, in order to ensure the stability of the cell and inhibit the degree of crack propagation, the operating temperature of the cell should not be lower than 1023 K, and the coefficient of thermal expansion of anode should be less than 12.50×10 ^-6K ^-1. In addition, when the pre-crack angle is 45° or the pre-crack is 0.45mm away from the bottom of anode, the maximum width after crack propagation is the smallest, and the propagation path is the most predictable. In this case, the cell is affected by the smallest crack range and the highest stability. This research provides a guidance for suppressing crack propagation in solid oxide fuel cell, improving the lifetime and promoting the commercialization process of fuel cell.