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High‐speed elongating metal jets, such as are produced by shaped charges, are known to break up into a number of fragments after some stretching. Attempts to explain the lengths of the segments have usually related to Rayleigh’s work on the separation of a jet of water into droplets as a result of surface tension and on extensions of that work, although more recently research based on the ideas of plastic flow has had some success in showing the growth of instabilities of approximately correct wavelength. In this paper, the full equations of axially symmetric plastic flow are used, along with the von Mises condition, and a series solution sought to first order in a small parameter Y/ρW2, where Y is the yield strength of the metal, ρ its density, and W the fall in velocity along the jet. The disturbances to velocity, shear stresses, and boundary oscillation arising from an initial small disturbance in the axial component of velocity have been found analytically. The results show that the amplitudes of the disturbances grow towards equality with the radius of the elongating jet for times and wavelengths compatible with observations of break up. Two possible criteria for break up are examined: namely, ‘‘necking’’ and the creation of voids in the jet when all principal stresses become tensile. There is radiographic evidence that both kinds of break up can occur. The results obtained here confirm the significance of these mechanisms, but are not able to distinguish sufficiently between them as the prime cause of break up in a given instance.