Upon stretching the lung during inspiration, the parenchymal tissue stores elastic energy in the form of a recoil force that helps lung volume return to functional residual capacity during expiration. This recoil force arises largely as a result of the stretching of collagen and elastic fiber networks together with the expansion of the surface film at the air-liquid interface. Linking the elastic properties of the parenchyma to the lung’s multi-scale structures requires complex models based on the anatomic realities of the extracellular matrix. For example, unfolding and recruiting wavy collagen fibers greatly stiffens the tissue as it inflates toward total lung capacity. However, modeling predicts an instability during inflation leading to a runaway phenomenon at high transpulmonary pressures. At low pressures, the network properties of the parenchyma are also influenced by proteoglycans. Lung elasticity in all its manifestations is thus impossible to address in a quantitative fashion without the use of rather sophisticated mathematical and computational models. Predictions provided by such computational models can provide important insights into the nature of fundamental physiologic and biologic processes in the presence of gravity as well as how these processes become deranged in disease.