The closure of a human lung airway is modeled as a pipe coated internally with a liquid. For a thick enough coating, the Plateau-Rayleigh instability creates a liquid plug which blocks the airway halting distal gas exchange. This airway closure fow induces high stress levels on the wall, which is the location of airway epithelial cells. The bi-frontal plug growth induces a high level of stress and stress gradients on the epithelial cells, which are large enough to damage them, causing sub-lethal or lethal responses. We simulate the effect of the viscoelastic properties of mucus by means of the Oldroyd-B model. Increasing the relaxation time speeds up the airway closure and, if the solvent concentration is low enough, the extra stresses induce a second lethal response of the epithelial cells because of an elastic instability. The effect of surfactant is also investigated and becomes relevant only if the surfactant concentration is high enough, causing a delay of the closure and a decrease of wall stresses.