Under the assumption that the viscosity coefficient is in inverse proportion to the power law of the equivalent plastic strain rate. The friction touch effect between viscosity and crack-tip surfaces is considered, the asymptotic solution is established for elastic-viscoplastic field at the mixed-mode quasi static crack-tip under compression and shear. The numerical solution at crack-tip without stress and stain gap is obtained. The variation of numerical solution is discussed for the mixed-mode under compression and shear according to each parameter. Through numerical results and analysis for the mixed-mode crack-tip field under compressing and shear, it is whole plastic without elastic unloaded section, viscosity effect is an important factor when propagating crack-tip field.