Failure mechanisms of materials are intrinsically intertwined with nonhomogeneity and randomness at fine scales. By using mean field data for heterogeneous materials, homogeneous materials-based fracture models might result in prediction of unrealistic smooth crack trajectories and consequently unreliable load-carrying capacity. This study aims to develop a heterogeneous cohesive (HC) crack model to predict macroscopic strength of materials based on meso-scale random fields of fracture properties. By characterizing spatially varying fracture properties as random fields, heterogeneous cohesive crack propagation is simulated to predict more realistic crack paths and to more reliably assess macroscopic load-carrying capacity. A new stress-based criterion to determine the crack growth direction is developed by taking into account both the crack-tip stress state and heterogeneity of the tensile strength. A concrete beam subjected to mixed-mode fracture is modelled as a benchmark example to demonstrate the HC crack model. The numerical simulation reveals that crucial fracture phenomena, such as the tortuousness in crack trajectories, can be effectively captured by the HC model. Effects of various important parameters on the crack paths, peak loads, macroscopic ductility and overall reliability, including the variance of random fields, the correlation length, and the shear fracture resistance, are investigated and discussed. Criticality of the crack propagation incremental length in fracture modelling of random heterogeneous materials is especially highlighted. (C) 2008 Elsevier B.V. All rights reserved.