Underlying the nuclear envelope (NE) of most eukaryotic cells is the nuclear lamina, a meshwork consisting largely of coiled-coil nuclear intermediate filament proteins that play a critical role in nuclear organization and gene expression, and are vital for the structural stability of the NE/nucleus. By confocal microscopy and micromanipulation of the NE in living cells and isolated nuclei, we show that the NE undergoes deformations without large-scale rupture and maintains structural stability when exposed to mechanical stress. In conjunction with image analysis, we have developed theory for a two-dimensional elastic material to quantify NE elastic behaviour. We show that the NE is elastic and exhibits characteristics of a continuous two-dimensional solid, including connections between lamins and the embedded nuclear pore complexes. Correlating models of NE lateral organization to the experimental findings indicates a heterogeneous lateral distribution of NE components on a mesoscopic scale.