Studying how epithelia respond to mechanical stresses is key to understanding tissue shape changes during morphogenesis. Here, we study the viscoelastic properties of the Drosophila wing epithelium during pupal morphogenesis, by quantifying mechanical stress and cell shape as a function of time. We find a delay of 8 hours between maximal tissue stress and maximal cell elongation indicating a viscoelastic deformation of the tissue. We show that this viscoelastic behaviour emerges from the mechanosensitivity of endocytic E-Cadherin turnover. The increase in E-Cadherin turnover in response to stress is mediated by mechanosensitive relocalization of the E-Cadherin binding protein p120 Catenin from cell junctions to cytoplasm. Mechanosensitivity of E-Cadherin turnover is lost in p120 mutant wings, where E-Cadherin turnover is constitutively high. In this mutant, the relationship between mechanical stress and cell elongation is altered. Cells deform more rapidly in response to stress , indicating a lower viscosity. Unlike wild type, p120 mutant cells deform rapidly, reverting to their original shape when stress is relaxed. Taken together, our findings reveal that p120-dependent mechanosensitive E-Cadherin turnover regulates viscoelastic behaviour of epithelial tissues, allowing mechanical stresses to generate stable cell shape changes during development.