Chronic Obstructive Pulmonary Disease (COPD) is a chronic and progressively debilitating fatal lung disease. Although much is now known about COPD pathogenesis and progression, current treatments are not curative. Computational modeling has a significant role to play in elucidating the link between structure and function in COPD, and in suggesting new approaches to therapy. Following a brief introduction to the pathogenesis and progression of COPD, this chapter describes several modeling approaches that have been proposed to address the biomechanical and pathological aspects of the disease. Little modeling has been proposed to describe airway inflammation and mucus production. Solid mechanics of the alveolar tissue has demonstrated the presence of stress concentrations. Various computational network models of the alveoli with and without gravity incorporate the observation that mechanical stresses can rupture the enzymatically weakened fibers and septal walls, which redistributes these stresses and increases the risk of further rupture in nearby alveoli. This positive feedback process leads to the characteristic microscale airspace enlargement as well as giant low-attenuation super clusters in CT images of COPD patients. Agent-based modeling can be invoked to incorporate more specific pathobiology of cellular mechanotransduction that remodels the alveolar tissue, allowing rupture to take place.