The dynamic failure of homogeneous and Functionally Graded Materials (FGMs) can be simulated by incorporating a Cohesive Zone Model (CZM) into the numerical scheme. The failure criterion is incorporated by the CZM using both a ßnite cohesive strength and work to fracture in the material description. In this study, ßrst the general dynamic behavior of FGMs (without initial crack) is investigated considering bulk material modeled with graded elements, i.e. elements possessing a spatially varying material property ßeld, such as Young's modulus, Poisson's ratio, mass density, etc. The results reveal some interesting features of dynamic behavior of FGMs compared to that of homogeneous materials. Next, two CZMs developed for FGMs are described and the numerical implementation scheme is discussed. Finally, the inàuence of material property variation on the crack propagation pattern for FGM structures under impact loading is investigated with a number of examples. The powerful features of CZMs in simulating branching and spontaneous crack initiation behaviors are also presented. The present ßnite element code is named I-CD (Illinois Cohesive Dynamic).