This paper aims at developing a random morphological model for concrete microstructures. A 3D image of concrete is obtained by microtomography and is used in conjunction with the concrete formulation to build and validate the model through morphological measurements. The morphological model is made up of two phases, corresponding to the matrix, or cement paste and to the aggregates. The set of aggregates in the sample is modelled as a combination of Poisson polyhedra of different scales. An algorithm is introduced to generate polyhedra packings in the continuum space. The latter is validated with morphological measurements.