Fundamental processes in development and physiology are determined by the three-dimensional architecture of epithelial sheets. How these sheets deform and fold into complex structures has remained unclear, however, because their mechanical properties in three-dimensions have not been accessed experimentally. By combining measurements of epithelial tension, shape, and luminal pressure with mathematical modeling, here we show that epithelial cell sheets are active superelastic materials. We develop a new approach to produce massive arrays of epithelial domes with controlled basal shape and size. By measuring 3D deformations of the substrate and curvature of the dome we obtain a direct measurement of luminal pressure and epithelial tension. Observations over time-scales of hours allow us to map the epithelial tension-strain response, revealing a tensional plateau over several-fold areal strain reaching 300%. We show that these extreme nominal strains are accommodated by a highly heterogeneous stretching of individual cells, with barely deformed cells coexisting with others reaching 1000% areal strain, in seeming contradiction with the measured tensional uniformity. This phenomenology is reminiscent of superelasticity, a mechanical response generally attributed to microscopic material instabilities in metal alloys. We provide evidence that this instability is triggered in epithelial cells by a stretch-induced dilution of the actin cortex and rescued by the intermediate filament network. Finally, we implement a mathematical model that captures both the tension/strain relationship and strain heterogeneity. Our study unveils a new type of mechanical behavior -active superelasticity- that enables epithelial sheets to sustain extreme stretching under constant tension.
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