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The equations governing the linearized stability of a perfectly plastic sheet that is isotropically stretching in the horizontal direction and accelerating in the vertical direction are analyzed. The stability of the sheet depends on two dimensionless parameters. The parameter Γ measures the ratio of the inertial forces to the plastic forces, and the parameter Π measures the importance of the pressure gradient induced by the stretching to the pressure gradient induced by the vertical acceleration. Both of these parameters decrease as the sheet stretches. When Π is small and Γ/Π is not, the sheet breaks up because of Rayleigh–Taylor instability. When both Π and Γ/Π are small, the sheet breaks up to the necking instability. The case where Π is large has already been covered in part I of this paper.