Abstract: Despite clear general progress with element-free Galerkin method (EFGM), its low computational efficiency becomes a technical issue in the simulation of realistic problems. To improve the efficiency of EFGM, a smoothed meshfree Galerkin method is presented for the 2D elasticity problem. In the method presented, displacement fields are constructed using the moving least square (MLS) approximation and strains are smoothed over two-level nesting smoothed triangular cells based on the generalized gradient smoothing technique. Then, the generalized smoothed Galerkin (GS-Galerkin) weak form is used to create the discretized system equations. Each two-level nesting smoothed triangular cells include the triangular background cell itself and four equal-area triangular sub-cells, respectively. According to the Richardson extrapolation method, an optimal combination of the two-level smoothed strains can be obtained. Since the present method uses the linear interpolation on the boundary of problem domain, the boundary conditions including the essential and natural boundary conditions can directly impose as that in FEM. Several examples, including the cantilever beam, infinite plate with a circle hole, infinite plate with a central crack and the twin-arched tunnel, are investigated to demonstrate the accuracy and efficiency of the present method. The numerical results show that with more smoothing sub-cells by using in the smoothed meshfree Galerkin method, higher numerical accuracy can be obtained. In addition, the present method is higher efficient than EFGM. As a consequence, the smoothed meshfree Galerkin method with two-level nesting smoothed triangular cells significantly outperforms the EFGM and is very successful and attractive numerical method for solving the elasticity problems.