Abstract: In order to overcome the practical difficulty of solving complex axisymmetric elasticity problems, the application of the meshless local Petrov-Galerkin (MLPG) method to solve the problems was studied, and the numerical method with the adaptive faculty was proposed. In the end, through several numerical examples, the present method was tested. The results show that the proposed method is available and effective to solve such problems, and the numerical solutions are also satisfactory.