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Metastasis is one of the greatest challenges in cancer treatment today. Normal mammary epithelial cells are optimally supported by interaction with a soft matrix (microenvironment) with elastic modulus of about 800 Pa. However, after transformation, breast tissue becomes progressively stiffer and tumour cells become significantly more contractile and hyper-responsive to matrix elasticity. In addition, importantly, the cancer cells penetrate into blood vessel and enter the circulation during metastasis. The modulus of fluid such as blood or mucus has very low stiffness of around 50 Pa. For this reason, the critical association between cancer cell phenotype and the change of matrix rigidity with an order of magnitude smaller should be emphasizing. This review highlights the current understanding of epithelial-mesenchymal transition and cancer stem cells in metastasis, and identified importance for investigation on artificial extracellular matrix with different viscoelastic properties, which is required to mimics in vivo microenvironment. The substrate damping coefficient (tand) as potential physical parameter emerged the important linkage to cellular motility, cancer stemness, and epithelial-mesenchymal transition induction. Although further investigation is required to clarify the efficacy of environmental stimuli (tand) for tumors exhibiting stem cell-like properties, this review indicates that the cancer cells incubated on softer substrate might lead to express cancer stem cell biomarkers exhibiting high expression.