Abstract: This paper proposes a method based on the physics-informed neural networks (PINN) for solving the thin-walled structure buckling problem. The governing equations of thin-walled buckling can be expressed as a fourth-order nonlinear partial differential equation system with the in-plane displacement and stress functions as variables. The PINN solution can overcome the dependence of traditional numerical methods on the mesh partition of the computational domain and conduct mesh-free calculations on the entire computational domain. The neural network model presented in the paper utilizes a weighted mean square error loss function composition for updating network parameters and employs the arc-length method for the outer-loop iteration control to deal with the iteration characteristic of buckling problems. The incorporation of the arc-length method, hard constraints, weight adjustment strategy based on trial-and-error pre-training, and self-adaptive activation function strategy enables PINN to solve linear and nonlinear buckling problems effectively. Two types of problems are investigated in the study, including buckling mode analysis and nonlinear post-buckling problems with geometry deficiencies. A comparison is made between the solutions obtained from the neural network and finite element results. The results demonstrate the efficacy of the proposed method in accurately solving both linear and nonlinear buckling problems in thin-walled structures, highlighting its potential applications in structural engineering and design optimization. The research results show that the physics-informed neural network can effectively analyze the buckling problem of thin-walled structures without requiring artificial preprocessing of the computational domain. Additionally, PINN retains the traditional characteristic of normal DNNs and can accept labeled data for faster calculations. The paper shows that the labeled buckling mode data can accelerate the convergence of the network. The drawback of PINN is that it converges slower than the mature finite element method, but the feature of requiring no artificial preprocessing of the solution domain before the training process makes PINN feasible in engineering.