Acute respiratory distress syndrome (ARDS) is a devastating cascade of deteriorating lung function characterized by fluid accumulation in the distal airways of the deep lung. During breathing, micron-sized bubbles of air propagate through these occluded airways, exerting abnormally-high hydrodynamic stresses on the cells that line the airway walls. The objective of this dissertation was to investigate the mechanical response of the cells to these injurious stresses through computational fluid-structure interaction models. Morphologically-accurate, 3D finite element models of alveolar epithelial cells were reconstructed from confocal microscopy images. Hydrodynamic stresses were calculated using the boundary element method. Results indicated that morphology has a significant influence on the risk of cell injury, with subconfluent cells developing higher membrane strains than confluent cells. Also, stiffening the cell membrane may have a protective effect on cells and this effect is more significant for confluent cells than subconfluent cells. To capture transient dynamic effects, a novel Prony-Dirichlet series constitutive formulation was developed for the soft glassy rheology (SGR) of cells, which is characterized by a weak power-law relationship between the complex shear modulus and frequency. The SGR model was used to show that maximum pressure gradient during airway reopening, not stress exposure duration, is responsible for cell injury as a consequence of the cells' soft glassy rheology properties. Furthermore, cell fluidization may mitigate cell injury. The SGR material formulation was extended to capture recently-reported timescale-dependent cell mechanics and results indicated that variations in the apparent power-law may arise from changes in the effective elasticity of the whole-cell cytoskeletal network. Finally, a finite element model of the oscillating optical tweezers microrheology technique showed that membrane mechanics contributions can increase apparent cell stiffness by up to two orders of magnitude. The modeling results were shown to be useful as a tool for suggesting future experimental studies of the effect of pharmacological agents on the risk of cell injury during ARDS. Advances in therapeutic treatments may lead to a reduction in ARDS-associated mortality and improved patient care.