Osmotic stress poses one of the most fundamental challenges to living cells. Particularly, the largely inextensible plasma membrane of eukaryotic cells easily ruptures under in-plane tension calling for sophisticated strategies to readily respond to osmotic stress. We describe how epithelial cells react and adapt mechanically to the exposure to hypotonic and hypertonic solutions in the context of a confluent monolayer. Site-specific indentation experiments in conjunction with tether pulling on individual cells have been carried out with an atomic force microscope to reveal spatio-temporal changes in membrane tension and surface area. We found that cells compensate for an increase in lateral tension due to hypoosmotic stress by sacrificing excess of membrane area stored in protrusions and invaginations such as microvilli and caveolae. At mild hypotonic conditions lateral tension increases partly compensated by surface are regulation, i.e. the cell sacrifices some of its membrane reservoirs. A loss of membrane–actin contacts occurs upon exposure to stronger hypotonic solutions giving rise to a drop in lateral tension. Tension release recovers on longer time scales by an increasing endocytosis, which efficiently removes excess membrane from the apical side to restore the initial pre-stress. Hypertonic solutions lead to shrinkage of cells and collapse of the apical membrane onto the cortex. Exposure to distilled water leads to stiffening of cells due to removal of excess surface area and tension increase due to elevated osmotic pressure across the plasma membrane.