Models of cellular and subcellular mechanics are essential in gaining an understanding of the link between forces applied to a cell and its biological response. Various approaches can be used to construct these models, but one that holds considerable promise is through the use of continuum solid and fluid mechanics, coupled when necessary with molecular dynamic simulations. Here we present a continuum mechanics model of the effects of normal stress applied to a layer of airway epithelial cells. The model predicts widely differing stress distributions associated with basolateral membrane deformation, intercellular flow, or mechanical forcing by other methods such as in the use of adherent beads. When coupled with experimental results obtained from cell culture, these simulations can help to identify the site and possibly the underlying mechanisms of mechanotransduction. We also present some hypotheses concerning the nature of mechanotransduction at the molecular scale.