Large nuclear deformations during migration through conned spaces have been associated with nuclear membrane rupture and DNA damage. However, the stresses associated with nuclear damage remain unclear. Here, using a quasi-static plane strain nite element model, we map evolution of nuclear shape and stresses during conned migration of a cell through a deformable matrix. Plastic deformation of the nucleus observed for a cell with sti nucleus transiting through a stier matrix lowered nuclear stresses, but also led to kinking of the nuclear membrane. In line with model predictions, transwell migration experiments with brosarcoma cells showed that while nuclear softening increased invasiveness, nuclear stiening led to plastic deformation and higher levels of DNA damage. In addition to highlighting the advantage of nuclear softening during conned migration, our results suggest that plastic deformations of the nucleus during transit through sti tissues may lead to bending-induced nuclear membrane disruption and subsequent DNA damage.