Epithelial monolayers are one-cell thick tissue sheets that separate internal and external environments. As part of their function, they have to withstand extrinsic mechanical stresses applied at high strain rates. However, little is known about how monolayers respond to mechanical deformations. Here, by subjecting suspended epithelial monolayers to stretch, we find that they dissipate stresses on a minute timescale in a process that involves an increase in monolayer length, pointing to active remodelling of cell architecture during relaxation. Strikingly, monolayers consisting of tens of thousands of cells relax stress with similar dynamics to single rounded cells and both respond similarly to perturbations of actomyosin. By contrast, cell-cell junctional complexes and intermediate filaments do not relax tissue stress, but form stable connections between cells, allowing monolayers to behave rheologically as single cells. Taken together our data show that actomyosin dynamics governs the rheological properties of epithelial monolayers, dissipating applied stresses, and enabling changes in monolayer length. the Rosetrees Trust, the UCL Graduate School, the EPSRC funded doctoral training program CoMPLEX, and the European Research Council (ERC-CoG MolCellTissMech, agreement 647186 to GC). N.K. was in receipt of a UCL Overseas Research Scholarship. N.K. was supported by the Prof Rob Seymour Travel Bursary Fund for research visits to Barcelona. J.F. and A.B. were funded by BBSRC grant (BB/M003280 and BB/M002578) to G.