An elastic-viscoplastic constitutive model is proposed instead of the usual elastoplastic model. It is assumed that when crack-tip is approached the viscosity coefficient lends to zero (η=η0r). Asymptotic analysis of the dynamic field near a propagating crack-tip is given, and the uniparameter solution is obtained. The numerical result is given for various Mach number and viscosity coefficient. Based on the asymptotic solution, a fracture criterion is proposed and the stability of crack propagation is discussed.