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Abstract: A granular structure is usually modeled by a parallelepiped containing spherical balls in three dimensions or by a rectangle filled with disks in two dimensions. These grains (spherical balls or disks) are disjoint and their size correspond to a size distribution determined by experiments. In this paper, we consider the geometrical modeling and the meshing of these structures. To define the repartition of disjoint grains, we propose a new constructive algorithm based on an advancing-front approach. Often, the use of an advancing-front algorithm leads to a heterogeneity of the local density in the generated structure. In order to homogenize this density, we propose an optimization method based on local grain relocations. Furthermore, we introduce a method to transform spherical balls into polyhedral cells similar to realistic grain shapes. To generate quality meshes of granular models with, either spherical balls (disks) or polyhedral (polygonal) cells, an adaptive scheme is proposed. The mesh generation method is a combined advancing front-Delaunay approach governed by a metric field. The metric specification is based on the geometry and the proximity of grains. [Copyright &y& Elsevier]