Abstract: The meshless local Petrov-Galerkin(MLPG) methodis extended to solve the stability problems of an anisotropic plate withthe moving least-square (MLS) approximation to interpolate solutionvariables and Kirchhoff's plate theory. In the analysis, the essentialboundary conditions are enforced by a penalty method. The discreteeigenvalue problem is derived using the local integral symmetric weak formof the governing equation of stability problems. Several examples,isotropic and symmetrically laminated composite plates, are given andcompared with other methods to show that the MLPG method has a number ofadvantages such as the accuracy and the good convergence.