The composition of most engineering materials is heterogeneous at some degree. It is simply a question of scale at which the level of heterogeneity becomes apparent. In the case of cementitious granular materials such as concrete the heterogeneity appears at the mesoscale where it is comprised of aggregate particles, a hardened cement paste and voids. Since it is difficult to consider each separate particle in the topological description explicitly, numerical models of the meso-structure are normally confined to two-phase matrix particle composites in which only the larger inclusions are accounted for. 2-D and 3-D concrete blocks(Representative Volume Element, RVE) are used to simulating heterogeneous concrete meso-structures in the form of aggregates in the hardened mortar with nearly zero-thickness linear or planar interfaces. The numerical sensitivity of these meso-structures are Investigated with respect to the different morphologies of heterogeneity and the different level of coupling constant among fracture mode I, II and III. In addition, a numerically homogenized concrete block in 3-D using Hashin-Shtrikman variational bounds provides an evidence of the effective cracking paths which are quite different with those of heterogenous concrete block. However, their average force-displacement relationship show a pretty close match each other.