Abstract: The finite particle method (FPM) is a new structural analysis method which is based on the Vector Mechanics and numerical calculations. In this method, the analyzed domain is discretized into finite particles, whose motion follows Newton’s second law. The convected material frame is introduced to calculate the internal force of the structural element. To avoid iteration in solving nonlinear motion equations, the explicit time integration is adopted. This paper presents a buckling analysis of structures using FPM. Taking the three dimensional bar element as an example, the formulations of the FPM are derived in the paper. Structural buckling behaviors are simulated with the program based on the FPM algorithm. This method can reach the critical load and track post-buckling behaviors of structures without any special considerations. In addition, there is no need to apply structural loads gradually. All loads can be applied to the structures at the initial step of the analysis, which accords with the practical situation. Several numerical examples are presented to demonstrate the capabilities and accuracy of this method in the buckling analysis of structures.