Extension-induced crystallization under near-equilibrium condition has been studied in a series of lightly cross-linked high density polyethylene (XL-HDPE) with a combination of extensional rheology and in situ synchrotron radiation small-angle X-ray scattering (SAXS) and wide-angle Xray diffraction (WAXD) measurements. According to crystal morphology and structure, four regions were defined in strain-temperature space, namely "orthorhombic lamellar crystal" (OLC), "orthorhombic shish crystal" (OSC), "hexagonal shish crystal" (HSC) and "oriented shish precursor" (OSP), respectively. This indicates that flow not only induces entropic reduction of initial melt, but also modifies the free energies of the final states, which is overlooked in the classical stretched network model (SNM) for flow induced crystallization (FIG). Incorporating the free energies of various final states, a modified SNM is developed and employed to analyze strain-temperature equivalence on nucleation in FIG, which reveals that the critical nucleus thickness l* at different regions leads to a natural transition from lamellar to shish nuclei. The results suggest that classical nucleation theory is still valid for FIG under near-equilibrium condition provided that the free energy changes of initial melt and final states induced by flow are taken into account.