Lamin A is a nuclear intermediate filament protein critical for nuclear architecture and mechanics and mutated in a wide range of human diseases. Yet little is known about the molecular architecture of lamins and mechanisms of their assembly. Here we use SILAC cross-linking mass spectrometry to determine interactions within lamin dimers and between dimers in higher-order polymers. We find evidence for a compression mechanism where coiled coils in the lamin A rod can slide onto each other to contract rod length, likely driven by a wide range of electrostatic interactions with the flexible linkers between coiled coils. Similar interactions occur with unstructured regions flanking the rod domain during oligomeric assembly. Mutations linked to human disease block these interactions, suggesting that this spring-like contraction can explain in part the dynamic mechanical stretch and flexibility properties of the lamin polymer and other intermediate filament networks.