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In engineering and materials science, necking is a mode of tensile deformation where relatively large amounts of strain localize disproportionately in a small region of the material. The resulting prominent decrease in local cross-sectional area provides the basis for the name "neck". Because the local strains in the neck are large, necking is often closely associated with yielding, a form of plastic deformation associated with ductile materials, often metals or polymers. Once necking has begun, the neck becomes the exclusive location of yielding in the material, as the reduced area gives the neck the largest local stress. Necking results from an instability during tensile deformation when the cross-sectional area of the sample decreases by a greater proportion than the material strain hardens. Armand Considère published the basic criterion for necking in 1885, in the context of the stability of large scale structures such as bridges. Three concepts provide the framework for understanding neck formation. Before deformation, all real materials have heterogeneities such as flaws or local variations in dimensions or composition that cause local fluctuations in stresses and strains. To determine the location of the incipient neck, these fluctuations need only be infinitesimal in magnitude. During plastic tensile deformation the material decreases in cross-sectional area due to the incompressibility of plastic flow. (Not due to the Poisson effect, which is linked to elastic behaviour.) During plastic tensile deformation the material strain hardens. The amount of hardening varies with extent of deformation. The latter two effects determine the stability while the first effect determines the neck's location. Instability (onset of necking) is expected to occur when an increase in the (local) strain produces no net increase in the load, F. This will happen when This leads to with the T subscript being used to emphasize that these stresses and strains must be true values.

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