The nuclear lamina—a meshwork of intermediate filaments termed lamins—is primarily responsible for the mechanical stability of the nucleus in multicellular organisms. However, structural-mechanical characterization of lamin filaments assembled in situ remains elusive. Here, we apply an integrative approach combining atomic force microscopy, cryo-electron tomography, network analysis, and molecular dynamics simulations to directly measure the mechanical response of single lamin filaments in three-dimensional meshwork. Endogenous lamin filaments portray non-Hookean behavior – they deform reversibly at a few hundred picoNewtons and stiffen at nanoNewton forces. The filaments are extensible, strong and tough similar to natural silk and superior to the synthetic polymer Kevlar®. Graph theory analysis shows that the lamin meshwork is not a random arrangement of filaments but exhibits small-world properties. Our results suggest that lamin filaments arrange to form an emergent meshwork whose topology dictates the mechanical properties of individual filaments. The quantitative insights imply a role of meshwork topology in laminopathies.