Numerical Manifold Method (NMM) has gained widespread application in engineering practice due to its capacity to effectively address both continuous and discontinuous problems in a unified framework. With the advancement of 3D-NMM, there remains a deficiency in ready-made preprocessing tools. Hence, the generation of 3D manifold elements (MEs) is the primary prerequisite for 3D-NMM. In this study, a parallel algorithm to generate the MEs is proposed. Firstly, a novel 3D block identification algorithm is developed to improve the modeling efficiency. Then, 3D joint networks are simulated using the geological statistical results. Thirdly, the mathematical cover system is constructed using uniformly regular hexahedral meshes. Subsequently, the physical domain is cut using the Boolean algorithm to generate the related manifold blocks (MBs) and the Union-Find algorithm is used to determine the relationship of MBs with mathematical patches (MPs) and physical patches (PPs). The proposed program incorporates the OpenMP parallel library for CPU parallelization to enhance its efficiency and the OpenGL library is used to build a real-time visualization program. Finally, the proposed program is validated using several representative examples, and the obtained results demonstrate its efficient capability in generating MEs.