Random packing of particles has served as a topic of intense research in the chemical, physical, engineering, and material fields. The majority of previous works focused on the random packing models of spherical, cylindrical, and ellipsoidal particles, whereas little is known about polyhedral particles. In this article, a modeling study of the random packing of convex polyhedral particles is presented in detail, using an interparticle contact detection algorithm, a particle-to-container wall intersection detection algorithm, and a random sequential packing algorithm for hard particles, and the accuracy and efficiency of the contact detection algorithm are compared with those of methods from the literature. With the random packing model and a specified particle size distribution, mesostructure models of particulate composites with mono-/polydisperse particles were generated and validated by a sectioning analysis algorithm. Based on quantitative stereological theories and the sectioning analysis algorithm, the effects of particle shape on the mesostructures composed of the monodisperse and polydisperse particles were evaluated. Further, the statistical results were verified by validation against experimental results from the literature and theoretical results.