Abstract:The research history and current state of Mesh-free methods are firstly introduced.The principle of MLS method is described emphatically.Then derivational process of EFG method controlling equation of weak form is given.Finally two dimensional EFG methods are applied to typical problem of solid mechanics,that is,cantilever.EFG's results are compared with analytical solutions.Simulation experimental results show that EFG method is fairly good to handle problems in solid mechanics.