The alveolar septum consists of a skeleton of fine collagen and elastin fibers, which are interlaced with a capillary network. Its mechanical characteristics play an important role in the overall performance of the lung. An alveolar sac model was developed for numerical analysis of the internal stress distribution and septal displacements within the alveoli of both normal and emphysematic saline-filled lungs. A scanning electron micrograph of the parenchyma was digitized to yield a geometric replica of a typical two-dimensional alveolar sac. The stress-strain relationship of the alveolar tissue was adopted from experimental data. The model was solved by using commercial finite-element software for quasi-static loading of alveolar pressure. Investigation of the state of stresses and displacements in a healthy lung simulation yielded values that compared well with experimentally reported data. Alteration of the mechanical characteristics of the alveolar septa to simulate elastin destruction in the emphysematic model induced significant stress concentrations (e.g., at a lung volume of 60% total capacity, tensions at certain parts in an emphysematic lung were up to 6 times higher than those in a normal lung). The combination of highly elevated stress sites together with the cyclic loading of breathing may explain the observed progressive damage to elastin fibers in emphysematic patients.