The process of invasion is of special importance in cancer metastasis, the main cause of death in cancer patients. Cells typically penetrate a matrix by degrading it or by squeezing through pores. However, cell mechanics and forces applied by cells especially during the initial stages of metastatic penetration, as metastatic cells indent a substrate, are still unknown. We use a specialized technology to measure the strength of the cells, specifically the forces that cells apply to an impenetrable, synthetic 2-dimensional gel-matrix to focus only on mechanical-interactions; gels are non-degradable polyacrylamide with sub-micron pores. We show that single metastatic breast-cancer cells will apply force to an impenetrable gel, and indent it in attempted invasion, when the gel is in the appropriate stiffness range; benign cells do not indent the gels. The metastatic cells require gel-substrates to be soft enough to indent, yet stiff enough to grip and generate force on. Cells develop grip handles and pull the underlying gels inwards and upwards bringing the nucleus into the indentation concavity. We reveal a special coordinated role for the nucleus and the cytoskeleton when a single cell attempts to invade the impenetrable barrier. The actin, nucleus, and microtubules reorganize in sequence, with the actin at the leading edge of the cell. Cells repeatedly attempt penetration over several hours and then relocate, indicating an advanced mechano-transduction feedback loop. The systems and analysis approaches shown here reveal cell adaptation, force application mechanisms, and can potentially serve as a diagnostic/prognostic platform.