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The aggregate generation of concrete is one of the important problems in concrete mesoscopic mechanics. Firstly, the mesoscopic numerical model with spherical aggregates is obtained by the method of excluding the occupied space, and fully-graded concrete model of high aggregate content can be quickly generated. Then, based on the spherical aggregate model, the generation method of random convex polyhedral aggregates is proposed. Finally, a full-graded concrete model with spherical aggregates is shown in Case 1 and a cylindrical concrete model with random convex polyhedral aggregates is shown in Case 2. The result shows that the aggregates are equally distributed in the concrete models which can be used in the study of mesoscopic numerical calculation.