Abstract：Presented in this paper is a new formulation of the element-free Galerkin method for the boundary-value problems of solid mechanics in which the moving Kriging interpolation procedure is employed instead of moving least squared procedure to construct shape function. The proposed procedure is characterized by the feature that the shape function constructed by moving Kriging procedure possess the property of Kronecker d -function and the consistency property. At the same time，the specified essential boundary conditions can be easily implemented while displacement boundary conditions are not easily imposed in the conventional element-free methods. The fundamental theory of this procedure is illustrated；and mathematical formulations are given. Then numerical examples are analyzed by the proposed procedure；and the computed results are compared with other solutions to verify the effectiveness and accuracy of the proposed method.
