The plate structure has a wide range of applications in the fields of mechanical manufacturing, aerospace, marine engineering, and constructional engineering because of its excellent mechanical properties and flexible design, and its stability requirement has also become an important issue that cannot be ignored in the design process. The instability of plate is caused by the joint action of bending and torsional deformation, and the stability problem of the composed structure is relatively complex. There are many calculation formulas under the traditional theoretical framework, and it is impossible to conduct a comprehensive analysis. As a new theory, the finite particle method (FPM) has great advantages in the analysis of complex behaviors such as dynamics, nonlinearity and failure of structures. The finite particle method is used to make buckling analysis of the single plate and its composite structure under different conditions, which provides a guarantee for the optimal design of plate structure.