In the present paper, The error of numerical solutions of the element free Galerkin method (EFGM) is estimated to eveluate accuracy of the EFGM. A method of smoothing the distribution of nodes is applied to the relocation of all nodes in the domain of an analysis model. The nodal relocation method in which nodes are relocated using physical interbubble force called bubble meshing for the FEM is applied to the adaptive analysis. The node allocation after relocation have higher accuracy than the initial node allocation.