The generation of three-dimensional (3D) manifold element is a critical problem for analyzing with 3D numerical manifold method (NMM). The aim of this paper is to investigate the generation of 3D manifold element and then develop the corresponding program with the C++ programming language. With the method of generation of 3D manifold element

the vertices

oriented edges

loops

faces and shells are considered as the fundamental data structure of 3D block based on the oriented theorem of topology. The Boolean intersection operations of blocks and mathematical meshes are conducted to validate new blocks. The manifold elements are generated once the validity of new blocks is satisfied. The vertices of each mathematical mesh are considered as the mathematical covers of new manifold elements

and then the physical covers are generated by subdivision of mathematical covers. Case studies for blocks with concaves

hollow or finite structural surfaces are conducted by using Boolean intersection operations with corresponding mathematical meshes. Moreover

a selected rock slope with many finite discontinuities is used to verify the developed method

with which shows that complicated block with concaves

hollow or finite structural surfaces can be well dealt. This study provides an effective and reliable way to analyze complicated structures.