In this paper,we use the weak Galerkin (WG) finite element method to solve the mixed form linear elasticity problem.In the mixed form,we get the discrete of proximation of the stress tensor and the displacement field.For the WG methods,we define the weak function and the weak differential operator in an optimal polynomial approximation spaces.The optimal error estimates are given and numerical results are presented to demonstrate the efficiency and the accuracy of the weak Galerkin finite element method.