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The cell nucleus is constantly subjected to externally applied forces. During metazoan evolution, the nucleus has been optimized to allow physical deformability while protecting the genome under load. Aberrant nucleus mechanics can alter cell migration across narrow spaces in cancer metastasis and immune response and disrupt nucleus mechanosensitivity. Uncovering the mechanical roles of lamins and chromatin is imperative for understanding the implications of physiological forces on cells and nuclei. Lamin‐knockout and ‐rescue fibroblasts and probed nucleus response to physiologically relevant stresses are generated. A minimal viscoelastic model is presented that captures dynamic resistance across different cell types, lamin composition, phosphorylation states, and chromatin condensation. The model is conserved at low and high loading and is validated by micropipette aspiration and nanoindentation rheology. A time scale emerges that separates between dominantly elastic and dominantly viscous regimes. While lamin‐A and lamin‐B1 contribute to nucleus stiffness, viscosity is specified mostly by lamin‐A. Elastic and viscous association of lamin‐B1 and lamin‐A is supported by transcriptional and proteomic profiling analyses. Chromatin decondensation quantified by electron microscopy softens the nucleus unless lamin‐A is expressed. A mechanical framework is provided for assessing nucleus response to applied forces in health and disease., The cell nucleus is evolutionarily‐optimized to deform while protecting the genome under load. A viscoelastic model of nucleus resistance to physiologically relevant stresses that is conserved across cell types and nucleoskeletal perturbations is presented. An inherent timescale separates between elastic stretching set by lamin‐A and viscoelastic fluid deformation. Both A‐ and B‐type lamins contribute to steady‐state stiffness whereas lamin‐A and chromatin decondensation increase viscosity.