Potential metastatic cells can dissociate from a primary breast tumor by undergoing an epithelial-to-mesenchymal transmission (EMT). Recent work has revealed that cells in intermediate states of EMT acquire an augmented capacity for tumor-cell dissemination. These states have been characterized by molecular markers, but the structural features and the cellular mechanisms that underlie the acquisition of their invasive properties are still unknown. Using human mammary epithelial cells, we generated cells in intermediate states of EMT through the induction of a single EMT-inducing transcription factor, ZEB1, and cells in a mesenchymal state by stimulation with TGFβ. In stereotypic and spatially-defined culture conditions, the architecture, internal organization and mechanical properties of cells in the epithelial, intermediate and mesenchymal state were measured and compared. We found that the lack of intercellular cohesiveness in epithelial and mesenchymal cells can be detected early by microtubule destabilization and the repositioning of the centrosome from the cell-cell junction to the cell center. Consistent with their high migration velocities, cells in intermediate states produced low contractile forces compared with epithelial and mesenchymal cells. The high contractile forces in mesenchymal cells powered a retrograde flow pushing the nucleus away from cell adhesion to the extracellular matrix. Therefore, cells in intermediate state had structural and mechanical properties that were distinct but not necessarily intermediate between epithelial and mesenchymal cells. Based on these observations, we found that a panel of triple-negative breast cancer lines had intermediate rather than mesenchymal characteristics suggesting that the structural and mechanical properties of the intermediate state are important for understanding tumor-cell dissemination.