Probabilistic fracture analyses are performed for investigating uncertain fracture response of Functionally Graded Material (FGM) structures. The First-Order-Reliability-Method (FORM) is implemented into an existing Finite Element code for FGM (FE-FGM), which was previously developed at the University of Illinois at Urbana-Champaign . The computational simulation will be used in order to estimate the probability of crack initiation with uncertainties in the material properties only. The two-step probability analysis method proposed in the companion paper (Part I, ) is illustrated by a numerical example of a composite strip with an edge crack. First, the reliability index of a crack initiation event is estimated as we vary the mean and standard deviation of the slope and the location of the inflection point of the spatial profile of Young's modulus. Secondly, the reliability index is estimated as we vary the standard deviation and the correlation length of the random field that characterize the random spatial fluctuation of Young's modulus. Also investigated is the relative importance of the uncertainties in the toughness compared to those in Young's modulus.