Two non-Gaussian random field models are developed for characterizing the geometry of star-like inclusions in two-phase or multi-phase materials. For illustration, the models are calibrated to the geometrical features of a population of 128 similar ASTM C57 aggregates used in concrete. The first model is a sum of spherical harmonic functions with random non-Gaussian coefficients. The second model is a nonlinear memoryless mapping of a sum of spherical harmonic functions with Gaussian coefficients. The two random field models are used to develop Monte Carlo algorithms for generating virtual aggregates. By construction, the virtual aggregates capture essential statistics of the target population of aggregates. The performance of the proposed models is assessed by quantitative and qualitative metrics. (c) 2006 Elsevier B.V. All rights reserved.