Secretion of pulmonary surfactant by alveolar epithelial type II cells is vital for the reduction of interfacial surface tension, thus preventing lung collapse. To study secretion dynamics, rat alveolar epithelial type II cells were cultured on elastic membranes and cyclically stretched. The amounts of phosphatidylcholine, the primary lipid component of surfactant, inside and outside the cells, were measured using radiolabeled choline. During and immediately after stretch, cells secreted less surfactant than unstretched cells; however, stretched cells secreted significantly more surfactant than unstretched cells after an extended lag period. We developed a model based on the hypothesis that stretching leads to jamming of surfactant traffic escaping the cell, similar to vehicular traffic jams. In the model, stretch increases surfactant transport from the interior to the exterior of the cell. This transport is mediated by a surface layer with a finite capacity due to the limited number of fusion pores through which secretion occurs. When the amount of surfactant in the surface layer approaches this capacity, interference among lamellar bodies carrying surfactant reduces the rate of secretion, effectively creating a jam. When the stretch stops, the jam takes an extended time to clear, and subsequently the amount of secreted surfactant increases. We solved the model analytically and show that its dynamics are consistent with experimental observations, implying that surfactant secretion is a fundamentally nonlinear process with memory representing collective behavior at the level of single cells. Our results thus highlight the importance of a jamming dynamics in stretch-induced cellular secretory processes.