In this study, we conducted buckling analyses in metallic materials using the material point method (MPM)[1] and introduced graph neural networks (GNNs) to improve computational efficiency. Plastic buckling critically affects energy absorption performance and overall safety during collisions. Accurately assessing post-buckling load-bearing capacity and deformation is essential, especially for crash energy-absorbing components such as automotive crash boxes. Plastic buckling involves large deformations and material nonlinearity, requiring highly accurate and stable analysis methods. Although the finite element method (FEM) is widely used for structural analysis, post-buckling deformation often causes severe mesh distortion, resulting in numerical instabilities and convergence issues. To address these challenges, MPM, which integrates particles with a background grid, has attracted significant attention as a method that avoids mesh distortion and improves stability. MPM enables stable analysis of complex post-buckling behavior. This study applies MPM to analyze plastic buckling and evaluates its predictive capability by comparing the results with those from conventional FEM-based analyses, focusing on accuracy and stability. Although MPM provides stable solutions, it requires considerable computational resources. This limitation makes it challenging to apply MPM directly to practical design and optimization processes. Previous studies have introduced GNNs to reduce the computational cost of MPM in fluid and granular material simulations[2]. In applying GNNs to MPM, particles are modeled as nodes and their interactions as edges, enabling the network to approximate complex material responses efficiently. Unlike previous studies that focused on fluids and granular materials, this study applies GNNs to solid materials, which introduces additional challenges such as numerical fracture and boundary condition constraints. This study investigates whether machine learning-assisted MPM can accurately capture such highly nonlinear behavior while improving computational efficiency. REFERENCES [1] Sulsky, D. et al., A particle method for history-dependent materials. Computer methods in applied mechanics and engineering, Vol. 118 (1-2), pp. 179-196, 1994. [2] Sanchez-Gonzalez et al., Learning to simulate complex physics with graph networks. In International conference on machine learning pp. 8459-8468, 2020, November.