Geometry optimization using the elongation method is developed at the Hartree–Fock level of theory. The formalism of elongation energy gradient and its accuracy have been validated by model systems calcula- tions. The linear poly-hydrogen fluoride, polyethylene, planar polyacetylene and extended polyalanine are opti- mized using different basis sets and compared with con- ventional results. The results show that the elongation Hartree–Fock geometry optimization (ELG-HF-OPT) can reproduce conventional calculation results with high accuracy for various basis sets. For the poly-hydrogen fluoride calculation at 6-31G(d,p) basis set, moreover, ELG-HF-OPT gives a structure with lower ground state energy than conventional results with the same optimiza- tion convergence threshold. This means the potential pos- sibility of ELG-HF-OPT can locate a more stable structure than conventional calculations with the same optimization convergence criteria. Therefore, the ELG-HF-OPT would provide one more choice for performing optimization on complicated large systems.