DNA double-strand breaks drive genomic instability. However, it remains unknown how these processes may affect the biomechanical properties of the nucleus and what role nuclear mechanics play in DNA damage and repair efficiency. Here, we have used Atomic Force Microscopy to investigate nuclear mechanical changes, arising from externally induced DNA damage. We found that nuclear stiffness is significantly reduced after cisplatin treatment, as a consequence of DNA damage signalling. This softening was linked to global chromatin decondensation, which improves molecular diffusion within the organelle. We propose that this can increase recruitment for repair factors. Interestingly, we also found that reduction of nuclear tension, through cytoskeletal relaxation, has a protective role to the cell and reduces accumulation of DNA damage. Overall, these changes protect against further genomic instability and promote DNA repair. We propose that these processes may underpin the development of drug resistance.