Abstract: The asymptotic analysis of he stress and strain field at a propagating crack tip is given by means of an elastic-viscoplastic model. It is assumed that the viscosity effect can be neglected for elasticity strain, and only for plasticity strain, the viscosity is significant. By use of this model, the constitutive relations of a rate sensitive material and the dynamic equations of the stress and strain field a crack-tip are derived. The stress and strain singularity exponent of crack-tip field is given by mea...