The development of binder-jet sand-based 3D printing allows a quick design of complex parts for foundry molds. To ensure a good quality of casting, the mold must feature some specific mechanical, thermal and transport properties. In that context, a reliable modeling approach for the sand-core material provides a less expensive alternative to extended experimental campaigns. In the present paper, we propose a physics-based microstructure generation approach that is able to capture the experimentally observed anisotropy of the sand-binder composite. The corresponding packing algorithm features a directional contraction of the unit cell that mimics the layer-by-layer deposition of the sand. We also introduce an improved, grid-free approach to add binder between the grains. After the microstructure generation process, we compute the apparent stiffness and permeability on the generated microstructure, and show that these apparent properties are transversely isotropic in the vertical direction. We provide a parametric study on some parameters of interest, such as the volume fraction of binder or the layer thickness. Finally, the results obtained through our modeling approach are compared to experimental results available in the literature. These comparisons show that the anisotropy induced by our microstructure generation approach is similar to the one experimentally observed.