Abstract: In this paper, the singular weight function is introduced to modify the symmetric smoothed hydrodynamics (SSPH) approximation method firstly, which makes the shape functions constructed satisfy the Dirac delta function properties approximatively and the enforcement of essential boundary conditions become easier. Then, a new meshless Petrov-Galerkin method is proposed for solving elasticity problems by using the modified SSPH approximation method to construct trial function in local weak form with Heaviside weight function. Finally, several plane problems are calculated with the presented method. Numerical results demonstrate that the new method can achieve quite good accuracy and convergence.