Abstract: Under the condition that all the perfectly plastic stress components at a crack tip are the functions of θ only, making use of the Mises yield condition, steady-state moving equations and elastic perfectly-plastic constitutive equations, we derive the generally analytical expressions of perfectly plastic fields at a rapidly propagating plane-stress crack tip. Applying these generally analytical expressions to the concrete crack, we obtain the analytical expressions of perfectly plastic fields at the rapidly propagating tips of modes I and Ⅱ plane-stress cracks.