Abstract: Based on the generalized moving least square method, a new Element-Free Galerkin (EFG) double-variable approximation is applied to dynamic characteristic calculation and analysis of Euler beam. In the development of the approximation, displacement boundary conditions are imposed with penalty method, and mass matrix and stiffness matrix are created catering for the implementation of EFG. Natural frequencies and natural modes of four Euler beams with different boundary conditions are calculated by double-variable EFG. Comparing the proposed approximation with theoretical solution, finite element method (FEM) and single-variable EFG, it is concluded that the proposed approximation has higher interpolation precision and applicable to complicated boundary conditions. Especially, it is more accurate than FEM in higher modes. With trial method, the order of polynomial is discussed and then its reasonable value is given.