Abstract: The elastic mechanics analysis of axisymmetric structure cracks is an important and fundamental problem in engineering practice. Compared with the traditional finite element method, a new numerical method is proposed to improve the accuracy and efficiency of calculation, which has been widely concerned by scholars. This paper considers axisymmetric structures of regular external circular cracks with stress boundaries. The compatibility equation with boundary conditions is solved according to the elastic theory. The stress function is assumed to be a unified form of neural network. According to the differential relation between compatibility equation, boundary condition and the stress function. The neural network structures are respectively constructed by the compatible equation and stress boundary condition. Through multi-neural network combined training, network parameters are extracted. It solves the stress components. In this paper, a neural network method in polar coordinate system is proposed to solve the crack of axisymmetric structure. Numerical examples show that the proposed method has advantages over the traditional finite element method in both accuracy and efficiency.