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The existence of viscosity effect at the interface of double dissimilar materials has an important impact on the distribution of the interface crack-tip field and the properties variety of the interface itself.The singularity and viscosity are considered in the crack-tip.The elastic-viscoplastic governing equations of double dissimilar materials at the interface crack-tip field are established.The displacement potential function and boundary condition of interface crack-tip are introduced.The numerical analysis of elastic-viscoplastic/rigid interface for mode Ⅲ is 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 the interface propagating in the crack-tip field,and the interface crack-tip is a viscoplastic field governed by the viscosity coefficient,Mach number (Ma),and singularity exponent.