Under the context of subterranean formation modeling using finite volume methods, the computational domain is a basin, a reservoir, or an underground CO2 storage site. Such a domain has a layered structure and is geometrically described by its layer limits called horizons and random disruption of layers called faults. Horizons and faults are both numerically represented by 3D triangulated surface meshes. Respecting the interface formed by horizons and faults, the volume mesh of the subterranean formation is required to be mainly hexahedral, with a few tetrahedrons, prisms or pyramids allowed along the faults, where mesh non-conformity is tolerated. A “constrained grid” approach is proposed to generate the so-desired mesh. Firstly, each horizon surface is unfolded with fault traces being sewn. Then, for each unfolded horizon, a regular grid with the same topology is generated from its boundary. Subsequently, node relocation and conditional grid refinement are applied to constrain fault traces to the grid. Afterwards, each grid is mapped back to its corresponding 3D horizon surface with fault nodes being split. Finally, a hex-dominant mesh is generated by connecting consecutive grids along corresponding nodes, with some elements cut into two by faults and degenerated into prisms, tetrahedrons, and pyramids. An optimization procedure is then applied to enhance the shape quality of the resulting 3D mesh.