The three-dimensional crack propagation is analyzed by the three-dimensional numerical manifold method (3D NMM) and the corresponding program with C++ is established. By taking the advantages of 3D NMM in crack propagation

only crack shells and manifold elements are required to be updated without the use of Heaviside function. According to the stress obtained from 3D NMM

the nonlocal crack tracing method is used to analyze the failure state of every crack tip. If failure occurs

the crack propagates along the direction perpendicular to the maximum principal stress. Quadrilateral or triangle tracing method is selected according to the situation during propagation. In order to make the deformed surface remain plane

triangulation of new generated face is needed. The edge crack

horizontal penny-shaped crack and inclined penny-shaped crack are simulated. It is feasible that simulating crack propagation with 3D NMM. Furthermore

the proposed method is suitable for cases of nonclosed and closed crack tip line and is also effective for the nonplanar 3D crack growth where the crack tip line is located in an element.