Abstract: The dynamic stress intensity factor was studied about the Griffith crack between elastic and visco-elastic layers in an infinite length strip under impact load. The controlling equations expressed by the displacement of elastic and viscoelastic materials were deduced separately after using Laplace and Fourier integral transforms of the basic equations. The displacements in the Laplace domain were obtained by inverse Fourier integral transform;uniting the constitutive and geometrical equations, the analytical expressions of stress in Laplace domain were derived. By defining a dislocation density function, the Cauchy singular integral equations were given according to the boundary conditions and the problem was reduced to algebraic equations using Chebyshev orthogonal polynomial; then it can be solved with the method of collocation dots in the Laplace domain. The time response of the dynamic stress intensity factor was calculated with the numerical method and the influence of material parameters on it was analyzed. The results show that the influence of the shear relaxation parameter on mode Ⅰ dynamic stress intensity factor is bigger than on mode Ⅱ ,and the influence of the swelling relaxation parameter is opposite.