The interdigitated gel (LβI) phase is one of the membrane phases of phospholipid molecules in which the hydrophobic tails of the phospholipid molecules penetrate the opposite leaflet of the bilayer. Recent molecular dynamics (MD) simulations have shown that interdigitation can take place as a phase transition from the liquid-ordered (Lo) phase to the LβI phase under stretching. However, there is still no conclusive experimental evidence for this process, so its existence remains controversial. In this study, to explain the transition from energy balance, we propose a free-energy model. The model consists of three energy components: the elastic deformation energy, surface energy at the bilayer-water interface, and interphase boundary energy. To determine the parameters of the model, we perform MD simulations of a stretched 1,2-dipalmitoyl- sn-glycero-3-phosphocholine/cholesterol bilayer. The phase diagrams from our model are in good agreement with those obtained from MD simulations. The energy balance among the components in the stretched bilayer quantitatively explains the stretch-induced transition. In the model, increasing the system size to that used in experiments shows that interdigitation is favorable for rigid bilayers under stretching or in alcohol solutions. These results suggest that the stretch-induced interdigitation might be observed in microscopic experiments.