In this work, we present a review of the elongation method, focusing on the linear-scaling implementation, which speeds up Hartree-Fock (HF) self-consistent field (SCF) calculations. The two important aspects of the elongation method for linear scaling are described. One is the so-called cutoff technique, which avoids the bottleneck of the conventional HF scheme, i.e., the number of 2e-integrals and the dimension of diagonalization. The other one is the QFMM method to finally achieve the linear scaling. Some test calculations show its good linear scaling for the elongation method.