A computational model of the human respiratory tract was developed to study airway and alveolar compression and re-expansion during deep breath-hold dives. The model incorporates the chest wall, supraglottic airway, trachea, branched airway tree, and elastic alveoli assigned time-dependent surfactant properties. Total lung collapse with degassing of all alveoli is predicted to occur around 235 m, much deeper than estimates for aquatic mammals. Hysteresis of the pressure-volume loop increases with maximum diving depth due to progressive alveolar collapse. Reopening of alveoli occurs stochastically as airway pressure overcomes adhesive and compressive forces on ascent. Surface area for gas exchange vanishes at collapse depth, implying that the risk of decompression sickness should reach a plateau beyond this depth. Pulmonary capillary transmural stresses cannot increase after local alveolar collapse. Consolidation of lung parenchyma might provide protection from capillary injury or leakage caused by vascular engorgement due to outward chest wall recoil at extreme depths.