Abstract: A torsional impact problem of a cylindrical crack in a functionally graded pipe is investigated. The shear modulus and mass density of the pipe are assumed to vary continuously. The mixed boundary value problem is first reduced to a singular integral equation with a Cauchy type kernel in the Laplace domain by applying Laplace and Fourier integral transforms and by introducing a dislocation density function. The singular integral equation is then solved numerically and the dynamic stress intensity factor (DSIF) in the physical domain is also obtained by a numerical inverse Laplace transform technique. Numerical results show that the DSIF rises rapidly to a main peak and then oscillates with a decreasing magnitude and tends to the corresponding static value, and that the crack position, thickness and material gradient of the pipe are able to influence significantly on the DSIF.