In the present paper, the mechanical model of dynamic propagation interface crack of the compression-shear mixed mode is proposed by using the elastic-viscoplastic constitutive model. Then the governing equations of propagation crack interface at crack tip are given. The numerical analysis is accomplished for the interface crack of compression-shear mixed mode by introducing a displacement potential function and some boundary conditions at interface crack tip. The distributed regularities of stress-strain fields of interface crack tip are discussed with several special parameters. 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.