Abstract: The elastic strain sofening-viscoplastic model is given in this paper. Using thismodel, the asymptotic Stress and strain equations surrounding the tip of a propagatingcrack are given and numerical results are obtained under antiplane shear. The analysisand calculation show that at the crack tip the Strain possesses logarithmic singularity(In(R/r))^1/(n+1) while the stress is like (In(R/r))^-n/(n+1), therefore theasymptotic behaviour of the elastic strain-sofening viscoplastic field is revealed underthe antiplane shear.