Abstract: The meshless local Petro-Galerkin method was applied to the calculation of two-dimensional elasticity mechanics problems by choosing properweight functions and basis functions. With the method, all integrals can be easily fulfilled on regular sub-domain boundaries, and to impose the essential boundary conditions, a penalty parameter can be used so that a positive definite and symmetric stiffnessmatrixmay be obtained. The comparison of its calculated resultwith that obtained using the ANSYS finite element method shows that the meshless method has the advantages such as high calculation accuracy, good stability and strong adaptability.