Biomechanical simulations are an important field of application for high performance computing due to the complexity and largeness of involved problems. This paper is concerned with coupled problems in the human respiratory system with emphasis on mechanical ventilation. In this context we focus on the modeling aspects of pulmonary alveoli and the lower airways. Our alveolar model is based on artificially generated random geometries and takes into account realistic tissue behavior as well as interfacial phenomena. On the part of the structural solver a smoothed aggregation algebraic multigrid method is used. For the first four generations of the bronchial tree, a geometry based on human computer tomography scans obtained from in-vivo experiments is employed. With the help of fluid-structure interaction simulations, flow patterns and airway wall stresses for normal breathing and mechanical ventilation of the healthy and diseased lung are investigated.