Constricted cell migration, which commonly occurs in vivo during tumor metastasis, can rupture nuclei. Associated rupture often correlates with high curvature imposed by pores, probes, or small micronuclei and with nuclear entry of chromatin-binding cGAS (cyclic-GMP-AMP synthase) from the cytoplasm. Suppression of lamin-A, a main component of the nuclear lamina, has been seen to increase rupture during constricted migration, but the dynamics of lamin-A under high curvature, and the mechanism by which lamin-A protects against rupture, remain incompletely understood. Thus, we studied the effect of curvature on lamin-A organization and nuclear rupture by passively pulling detached cells into micropipettes under controlled pressure. Additionally, using live imaging in highly elongated A549 human lung carcinoma cells, we quantified lamina dilution at pole regions of cell nuclei which underwent natural shape fluctuations. Extension of a nucleus into a micropipette caused dilution of lamin-B at the leading tip of the nucleus, proportional to aspirated length L, whereas dilution of lamin-A occurred only for L > Lcritical at the same early timepoint in aspiration. in similar experiments done with siLMNA U2OS human osteosarcoma cells transfected to express low or high levels of lamin-A-GFP (∼10-fold range), both low and high lamin-A levels required a critical strain to flow. Low levels of lamin-A showed greater lamin-A dilution and more nuclear rupture versus high levels as determined by cGAS entry and chromatin herniation. in highly elongated A549 cells, lamin-A at the high-curvature pole regions was found to be enriched relative to lamin-B, consistent with the idea that stiff elastic lamin-B responds immediately to applied stress while viscous lamin-A responds above some threshold. Lamin-A requires a critical strain rate to flow, and, importantly, nuclear rupture occurs at or above this critical dilution in lamin-A.