Abstract: The elongation method, originally proposed by Imamura was further developed for many years in our group. As a method towards O(N) with high efficiency and high accuracy for any dimensional systems. This treatment designed for one-dimensional (1D) polymers is now available for three-dimensional (3D) systems, but geometry optimization is now possible only for 1D-systems. As an approach toward post-Hartree-Fock, it was also extended to MP2 (ELG-LMP2) level. For the applications to large bio-systems, we applied it to DNA, random peptides, entangled insulin, linear or ring porphyrin wires and confirmed for any type of calculation path that the elongation method has very high accuracy, 10-8 a.u./atom error in total energy compared to the conventional direct calculations. The most remarkable feature of this method is to be applicable to large systems for which conventional direct SCF cannot be converged. Ill present the basic concept of elongation method and show some applications for nano- and bio-large systems.