This paper presents a Cohesive Zone Model (CZM) approach for investigating dy- namic failure processes in homogeneous and Functionally Graded Materials (FGMs). The failure criterion is incorporated in the CZM using both a ßnite cohesive strength and work to fracture in the material description. A novel CZM for FGMs is explored and incorporated into a ßnite element framework. The material gradation is approximated at the element level using a graded element formulation. A numerical example is provided to demonstrate the eácacy of the CZM approach, in which the inàuence of the material gradation on the crack branching pattern is studied.