Based on both the error estimates of moving least-square approximation in the Sobolev space Wk,p(Ω) and the continuity and coercion of the bi-linearity in the weak form of the elasticity, the error analysis of element-free Galerkin method for elasticity is discussed in this paper, the relationship between the error and the radius of the weight function is given, and the theorem of the error estimate presented. The error estimate proves to be of optimal order when nodes and shape functions satisfy some conditions. From the error analysis, it is shown that the error bound of the elasticity is directly related to the radius of the weight function. And a numerical example is given to verify the correctness of the given results.