In asthma, the contraction of the airway smooth muscle and the subsequent decrease in airflow involve a poorly understood set of mechanical and biochemical events. Organ-level and molecular-scale models of the airway are frequently based on purely mechanical or biochemical considerations and do not account for physiological mechanochemical couplings. Here, we present a microphysiological model of the airway that allows for the quantitative analysis of the interactions between mechanical and biochemical signals triggered by compressive stress on epithelial cells. We show that a mechanical stimulus mimicking a bronchospastic challenge triggers the marked contraction and delayed relaxation of airway smooth muscle, and that this is mediated by the discordant expression of cyclooxygenase genes in epithelial cells and regulated by the mechanosensor and transcriptional co-activator Yes-associated protein. A mathematical model of the intercellular feedback interactions recapitulates aspects of obstructive disease of the airways, which include pathognomonic features of severe difficult-to-treat asthma. The microphysiological model could be used to investigate the mechanisms of asthma pathogenesis and to develop therapeutic strategies that disrupt the positive feedback loop that leads to persistent airway constriction.