Abstract: Meshless local Petrov-Galerkin(MLPG) method is extended to solve buckling problems of a thin plate.The method uses the moving least-squares approximation to interpolate the solution variables,and employs a local symmetric weak form.The present method is a truly meshless one as it does not need any meshgrids,and all integrals can be easily evaluated over regularly shaped domains(in general,spheres in the three-dimensional problem) and their boundaries.The essential boundary conditions are enforced by a penalty method.Several examples are given to show that in solving buckling problems,the meshless local Petrov-Galerkin method still possesses some advantages such as good stability,high accuracy and high rate of convergence,just as in solving elastic static problems.