Abstract: Under the condition that all the perfectly plastic stress components at a crack tip are the functions of B only, making use of the Tresca yield condition, steady-state motion equations and elastic perfectly-plastic constitutive equations, we derive the general analytic eapressions of perfectly plastic stress field at a rapidly propagating plane-stress crack tip, Applying these general analytic eapressions to the concrete crack, we obtain the analytic expressions of perfectly plastic stress fields at the rapidly propagating tips of Modes Ⅰ and Ⅱ plane-stress cracks.