ABSTRACT Cancer cells are softer than the normal cells, and metastatic cells are even softer. These changes in biomechanical properties contribute to cancer progression by facilitating cell movement through physically constraining environments. To identify properties that enabled passage through physical constraints, cells that were more efficient at moving through narrow membrane micropores were selected from established cell lines. By examining micropore-selected human MDA MB 231 breast cancer and MDA MB 435 melanoma cancer cells, membrane fluidity and nuclear elasticity were excluded as primary contributors. Instead, reduced actin cytoskeleton anisotropy, focal adhesion density and cell stiffness were characteristics associated with efficient passage through constraints. By comparing transcriptomic profiles between the parental and selected populations, increased Ras/MAPK signalling was linked with cytoskeleton rearrangements and cell softening. MEK inhibitor treatment reversed the transcriptional, cytoskeleton, focal adhesion and elasticity changes. Conversely, expression of oncogenic KRas in parental MDA MB 231 cells, or oncogenic BRaf in parental MDA MB 435 cells, significantly reduced cell stiffness. These results reveal that MAPK signalling, in addition to tumour cell proliferation, has a significant role in regulating cell biomechanics. This article has an associated First Person interview with the first author of the paper.