As a first step towards particle-scale modeling of clayey soils, we investigate the mechanical behavior and microstructure of assemblies of three-dimensional rectangular platy particles by means of the discrete element method. Several samples composed of particles of different levels of platyness (ratio of width to thickness) were numerically prepared and sheared to large deformations. We analyze the shear strength, packing fraction, connectivity, contact and force anisotropies, and mobilization of friction forces as functions of platyness.We find that both the mechanical behavior and microstructure are strongly dependent on the degree of platyness. This happens, in particular, because of the alignment of particle faces along a particular direction. Additionally, as observed for other granular materials with complex shapes, the packing fraction passes by a peak value before decreasing for larger values of platyness.