The existence of viscosity effect at the interface of double dissimilar materials has an important impact to the distribution of interface crack-tip field and the properties variety of the interface itself. The singularity and viscosity are considered in crack-tip, and the elastic-viscoplastic governing equations of double dissimilar materials at interface crack-tip field are established. The displacement potential function and boundary condition of interface crack-tip are introduced, and the numerical analysis of elstic-viscoplastic/rigid interface for mode I are worked out. The stress-strain fields are obtained at the crack-tip and the variation rules of solutions are discussed according to each parameter. The numerical results show that the viscosity effect is a main factor of interface propagating at crack-tip field, and the interface crack-tip is a viscoplastic field that is governed by viscosity coefficient、Mach number and singularity exponent.