Abstract Meshing rock samples with sheet-like structures based their CT scanned volumetric images, is a crucial component for both visualization and numerical simulation. In rocks, fractures and veins commonly exist in the form of sheet-like objects (e.g. thin layers and distinct flat shapes), which are much smaller than the rock mass dimensions. The representations of such objects require high-resolution 3D images with a huge dataset, which are difficult and even impossible to visualize or analyze by numerical methods. Therefore, we develop a microscopic image based meshing approach to extract major sheet-like structures and then preserve their major geometric features at the macroscale. This is achieved by the following four major steps: (1) extracting major objects through extending, separation and recovering operations based on the CT scanned data/microscopic images; (2) simplifying and constructing a simplified centroidal Voronoi diagram on the extracted structures; (3) generating triangular meshes to represent the structure; (4) generating volume tetrahedron meshes constrained with the above surface mesh as the internal surfaces. Moreover, a shape similarity approach is proposed to measure and evaluate how similar the generated mesh models to the original rock samples. It is applied as criteria for further mesh generation to better describe the rock features with fewer elements. Finally, a practical CT scanned rock is taken as an application example to demonstrate the usefulness and capability of the proposed approach.