The cell nucleus is a mechanically responsive structure that governs how external forces affect chromosomes. Chromatin, particularly transcriptionally inactive heterochromatin, resists nuclear deformations through its mechanical response. However, chromatin also exhibits liquid-like properties, casting ambiguity on the physical mechanisms of chromatin-based nuclear elasticity. To determine how heterochromatin strengthens nuclear mechanical response, we performed polymer physics simulations of a nucleus model validated by micromechanical measurements and chromosome conformation capture data. The attachment of peripheral heterochromatin to the lamina is required to transmit forces directly to the chromatin and elicit its elastic response. Thus, increases in heterochromatin levels increase nuclear rigidity by increasing the linkages between chromatin and the lamina. Crosslinks within heterochromatin, such as HP1