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 derived. The equations are analyzed for the case where the vertical acceleration is zero. The stability of the sheet depends on a dimensionless parameter Γ that measures the ratio of the inertial forces to the plastic forces. This parameter decreases as the sheet stretches. The sheet is stable provided Γ is large. When Γ is small, the sheet is unstable to symmetrical disturbances. There is no sharply defined most unstable wavelength, but the most unstable wavelengths range between 10 and 1/Γ times the thickness of the sheet.