We introduce a stochastic 3D microstructure model for polycrystalline materials that exhibit crystallographic twins [1]. The model distinguishes between two types of twins, so-called neighboring twins and inclusion twins. While these two types of twins are similar with respect to their crystallographic properties, they significantly differ in their morphology. Neighboring twins are defined as two adjacent grains, sharing a Σ3 twin boundary, while inclusion twin pairs consist of a child grain predominantly surrounded by its parent grain. The present model initially calibrated for γ-TiAl, is versatile and applicable to numerous alloys and metals such as copper and nickel. The hierarchical model involves three key steps. First, the random grain architecture of the artificial polycrystal is generated by Laguerre tessellations on random point patterns. In the second step, pairs of neighboring twins are introduced, considering the spatial orientation of their joint grain boundary. Finally, inclusion twins are incorporated into random parent grains, modifying the initial morphology of the polycrystal. Combining the proposed model with numerical simulations of mechanical properties enables for investigating the impact of two different types of twins on the elastic [1] and plastic [2] response of polycrystalline materials. Additionally, it serves as a tool for generating training data for physics-informed neural networks. The latter will be addressed in the talk Self-supervised physics-informed surrogate model for elastic local fields in polycrystals by Lucas Monteiro Fernandes. [1] P. Rieder, M. Neumann, L. Monteiro Fernandes, S. Blusseau, A. Mulard, H. Proudhon, F. Willot, V. Schmidt. Stochastic 3D microstructure modeling of twinned polycrystals for investigating the mechanical behavior of γ-TiAl intermetallics. (working Paper) [2] L. Monteiro Fernandes, P. Rieder, M. Neumann, A. Mulard, H. Proudhon, V. Schmidt, F. Willot. Effect of crystallographic twins on the elasto-plastic response of polycrystals. (working Paper)