The two dimensional Meshless local Petrov-Galerkin method (MLPG) was expanded to three dimensional theory, and its codes were programmed in Fortran. Then, two classical numerical examples, the cube under uniform tension and the 3D cantilever beam, were calculated, and the results of MLPG3D were compared with the results of analytic theory and three dimensional finite element method (FEM). The results have shown the feasibility and effectiveness of MLPG for solving three dimensional elasto-static problems, and the precision of the results is better than those of FEM.