Abstract: The existence of viscosity effect at the interface ofdouble dissimilar materials has an important impact to the distribution ofinterface crack-tip field and the properties variety of the interfaceitself. The singularity is considered in crack-tip, and theelastic-viscoplastic governing equations of double dissimilar materials atinterface crack-tip field are established. The displacement potentialfunction and boundary condition of interface crack-tip are introduced, andthe numerical analysis of rigid-elastic viscoplastic interface for mode Iwas worked out. The stress-strain fields are obtained at the crack-tip andthe variations of solutions are discussed according to each parameter. Thenumerical results show that the viscosity effect is a main factor ofinterface propagating crack-tip field, and the interface crack-tip iselastic-viscoplastic field that is governed by viscosity coefficient, Machnumber and singular factor.