Abstract: Element-Free Galerkin Method (EFG) is a typical meshless method. Compared with others, meshless methods EFG method has simple, definite form, and can achieve highly accurate solution. There are also several notable advantages in the applications of EFG method, such as only required discrete nodal data, higher order continuity of the solutions, being able to represent high-gradient stress field and to track the spread process of crack propagation. At present, EFG method has become a study issue in computational mechanics field. This paper is concerned with the EFG method. Some major problems in EFG, such as choosing base function, determining radius of domain of influence, introducing essential boudary conditions, and so on, are addressed. Meanwhile, many results of applications of EFG are introduced. Finally, the prospect of EFGs development is discussed.