In recent years, the object for numerical analysis becomes complicated and the meshing is more and more difficult. The Free Mesh Method, which is one of the mesh-less methods, is considered to make large-scale analysis easier without the so-called meshing method. Enriched Free Mesh Method is a method based on Free Mesh Method. Analysis result of Enriched Free Mesh Method becomes better than analysis result of Free Mesh Method. In recent years, frequent re-mesh is required of n umerical analysis. However mesh generation still needs mush computation time. In order to reduce the computation time for meshing, we develop a new method using semi-circle with searching circle of nodes when employing the Free Mesh Method.