To divide in a tissue, both normal and cancer cells become spherical and mechanically stiffen as they enter mitosis. We investigated the effect of oncogene activation on this process in normal epithelial cells. We found that short-term induction of oncogenic Ras^V12 activates downstream mitogen-activated protein kinase (MEK-ERK) signaling to alter cell mechanics and enhance mitotic rounding, so that Ras^V12-expressing cells are softer in interphase but stiffen more upon entry into mitosis. These Ras^V12-dependent changes allow cells to round up and divide faithfully when confined underneath a stiff hydrogel, conditions in which normal cells and cells with reduced levels of Ras-ERK signaling suffer multiple spindle assembly and chromosome segregation errors. Thus, by promoting cell rounding and stiffening in mitosis, oncogenic Ras^V12 enables cells to proliferate under conditions of mechanical confinement like those experienced by cells in crowded tumors.