The mechanical properties of cells are increasingly recognized as directing physiology and pathology. Cancer metastasis in particular has emerged as a mechanically phenotyped disease, with consistent trends in single cell mechanics correlating with metastatic potential. However, how tissue-level mechanics change during early metastasis remains largely unexplored. We introduce a new methodology, Cell Monolayer Deformation Microscopy (CMDM), to quantify the mechanics of adherent cell monolayers; we use this methodology to reveal that during the Epithelial to Mesenchymal Transition (EMT) cell monolayers become stiffer, but also display more viscoelastic flow and are more brittle. This offers new insight into the mechanical stability of multicellular structures in development and disease.