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Epithelial–mesenchymal transition is associated with migration, invasion, and metastasis. The translation at the tissue scale of these changes has not yet been enlightened while being essential in the understanding of tumor progression. Thus, biophysical tools dedicated to measurements on model tumor systems are needed to reveal the impact of epithelial–mesenchymal transition at the collective cell scale. Herein, using an original biophysical approach based on magnetic nanoparticle insertion inside cells, we formed and flattened multicellular aggregates to explore the consequences of the loss of the metastasis suppressor NME1 on the mechanical properties at the tissue scale. Multicellular spheroids behave as viscoelastic fluids, and their equilibrium shape is driven by surface tension as measured by their deformation upon magnetic field application. In a model of breast tumor cells genetically modified for NME1, we correlated tumor invasion, migration, and adhesion modifications with shape maintenance properties by measuring surface tension and exploring both invasive and migratory potential as well as adhesion characteristics.