This paper describes an approach to generating the geometry in 3D of composite materials, taking the particular case of concrete. Concrete is presented as a particle array (aggregates) embedded in a matrix (mortar plus fine aggregates). Most of the earliest models consider the aggregates as spheres or ellipsoids, this is a fair approximation considering that the aggregates are oval-shaped but not good enough for crushed aggregates. For this reason, a realistic approach is proposed in which the aggregates are polyhedron-shaped taking into account the geometric description of a particular real sample. The method used to accomplish the generation is based on the Voronoï diagram, the algorithm used is presented and geometries up to 34% of aggregate fraction are included in the results and compared to actual concrete samples.