Abstract: In[1],under the condition that all the perfectly plastic stress components at a crack tip are functions of θ only,making use of equilibrium equations,stress-strain rate relations,compatibility equations and yield condition,Lin derived the general analytical expressions of the perfectly plastic stress field at a mixed-mode crack tip under plane and anti-plane strain.But in[1] there were several restrictions on the proportionality factor λ in the stress-strain rate relations,such as supposing that λ is independent of θ and supposing that λ=cor cr^-1.In this paper,we abolish these restrictions.The cases in[1],λ=crⁿ(n=0 or-1) are the special cases of this paper.