Finite element calculations are performed to model failure of a carbon/epoxy composite laminate loaded in tension in the through-thickness direction, and to predict the dependence of failure loads upon specimen size. The spatial variability of the inter-laminar strength is modelled by introducing different types of discrete random fields of material tensile strength. Fracture processes are modelled using the cohesive segment method, within the extended finite element framework of ABAQUS Standard. Monte Carlo Simulation are conducted on different realisations of the random fields; the predicted responses are compared to previously published measurements and to reference FE simulations, in which the material strength is taken as uniform and equal to the measured average. The comparison shows that the modelling approach presented here provides more accurate predictions of the structural failure loads and their dependence on size, as well as capturing the failure modes observed in experiments.