The lung has a very complicated porous structure composed of millions of alveoli. Modeling of the lung microstructure is important for various numerical analyses such as computation of stress distribution in the lung with mechanical ventilation. In this paper we have developed a new technique to model the lung microstructure using phase-field method. This method allows us to model varied structures by changing the numbers or shape of nuclei, which are the origins of alveoli. In addition, we have modeled the realistic structures of lung microstructure (alveolar duct and alveolar sac) by using columnar shaped nucleus. Moreover, we analyzed the local stress distribution in the lung microstructure model that is assumed to be inflated by ventilator. We found that the 3^<rd> principal stress is high near the connection of alveolar walls, the 1^<st> principal stress has no feature, and the 3^<rd> principal stress at the connection increases with the increase of the region volume or with the decrease of alveolar pressure.