Metastatic progression of tumors requires the coordinated dissemination of cancerous cells through interstitial tissues and their replication in distant body locations. Despite their importance in cancer treatment decisions, key factors, such as cell shape adaptation and the role it plays in dense tissue invasion by cancerous cells, are not well understood. Here, we employ a 3D electrohydrodynamic nanoprinting technology to generate vertical arrays of topographical pores that mimic interstitial tissue resistance to the mesenchymal migration of cancerous cells, in order to determine the effect of nuclear size, cell deformability, and cell-to-substrate adhesion on tissue invasion efficiency. The high spatial and temporal resolution of our analysis demonstrates that the ability of cells to deform depends on the cell cycle phase, peaks immediately after mitosis, and is key to the invasion process. Increased pore penetration efficiency by cells in early G1 phase also coincided with their lower nuclear volume and higher cell deformability, compared with the later cell cycle stages. Furthermore, artificial decondensation of chromatin induced an increase in cell and nuclear deformability and improved pore penetration efficiency of cells in G1. Together, these results underline that along the cell cycle cells have different abilities to dynamically remodel their actin cytoskeleton and induce nuclear shape changes, which determines their pore penetration efficiency. Thus, our results support a mechanism in which cell proliferation and pore penetration are functionally linked to favor the interstitial dissemination of metastatic cells.