Abstract: The viscosity of material is considered at propagating crack-tip. Under the assumption that the artificial viscosity coefficient is in inverse proportion to power law of the plastic strain rate, an elastic-viscoplastic asymptotic analysis is carried out for moving crack-tip fields in power-hardening materials under plane-strain condition. A continuous solution is obtained containing no discontinuities. The variations of numerical solution are discussed for mode I crack according to each parameter. It is shown that stress and strain both possess exponential singularity. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. And the tip field contains no elastic unloading zone for mode I crack. The quasi-static solution is recovered when the crack moving speed approaches zero, which show that the quasi-static solution is a special case of a dynamic one. If the limit case of zero hardening coefficient is further considered, the solution can be transformed to the elastic-nonlinear-viscous one of Hui and Riedel.