Abstract: Under the assumption that the artifical viscosity cofficient is in inverse proportion to power law of the plastic strain rate.The friction touch effection beween viscosity and crack-tip surface be considerde,the asymptotic solution is established for elastic-viscoplastic field at the mixed-mode propagating crack-tip under comprission and shear.The numerical solution to crack-tip without stress and stain gap is got. The variation of numerical solution are discussed for the mixed-mode under compression and shear according to each parameter.It is shown in numerical results and analysis that for the mixed-mode crack-tip field under compressing and shear is whole plastic without elatic unloaded section,viscosity effection is an important factor when propagating crack-tip field is studied, whether the mixed-mode crack trend to mode I or to mode II,the hydro-statil stresses are added according to the increasing on frictional coefficient. The crack-tip propagating velocity is prevented due to the frictoon on crack face,the tenacity on crack-tip freld become more higher with the more strorger on friction.Keywords: mixed-mode crack-tip under compression and shear; steadily propagating; viscosity effectionelastic-viscoplastic materials