This paper investigates the transient interface cracking between a functionally graded material (FGM) and an elastic substrate. Firstly, the mixed-boundary value problem is reduced to a typical strip to triple series equations by using Fourier integral-transform techniques. And then, application of boundary conditions reduces the solution of the mixed-boundary value problem to a singular integral equation with a Hilbert-type singular kernel. The resulting singular integral equation is solved numerically and the periodic cracks tip field is examined. Effects of crack spacing, material properties and FGM nonhomogeneity on stress intensity factors are investigated in detail. The results obtained have the reference value in the design and application of functionally graded materials.