A mechanical model of a fracturing viscoelastic material was developed to investigate viscous effects in a dynamically growing crack-tip field. It was shown that in the stable creep-growing phase,elastic deformation and viscous deformation are equally dominant in the near-tip field,and stress and strain have the same singularity,namely,(σ,ε ) ∝ r?1 /( n?1) . The asymptotic solution of separating variables of stress,stain and displacement in the crack-tip field was obtained by asymptotic analysis,and the resulting numerical value of stress and strain in the crack-tip field was obtained by the shooting method and the boundary condition of a mode I crack. Through numerical calculation,it was shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M . When n →∞,the asymptotic solution of a viscoelastic material can be degenerated into that of Freund’s elastic-ideally plastic material by analyzing basic equations. A mechanical model of a fracturing viscoelastic material was developed to investigate viscous effects in a dynamically growing crack-tip field. It was shown that in stable creep-growing phase, elastic deformation and viscous deformation are even dominant in the near-tip field, (σ, ε) α r · 1 / (n · 1). The asymptotic solution of separating variables of stress, stain and displacement in the crack-tip field was obtained by asymptotic analysis , and the resulting numerical value of stress and strain in the crack-tip field was obtained by the shooting method and the boundary condition of a mode I crack. Through numerical calculation, it was shown that the near-tip fields are mainly governed by the creep exponent n and Mach number M. When n → ∞, the asymptotic solution of a viscoelastic material can be degenerated into that of Freund’s elastic-ideally plastic material by analyzing basic equations.