We present an element free Galerkin method(EFGM) for nonlinear transient field involving phase change.It needs no element connectivity.Compared with other methods such as the finite element method(FEM),it is easy in tracking the growth of phase boundaries.Essential boundary conditions are enforced using a penalty function method.The MATLAB codes are developed to obtain numerical solutions.Two classical examples show that,compared with the FEM,EFGM has more advantages such as high accuracy,good convergence and simple post-process,etc.