One major advantage of the numerical manifold method (NMM) is that it can solve the continuous and discontinuous problems in geomechanics in a unified way. It is not necessary to force the mathematical meshes to match the cracks in the NMM

which is very suitable for the simulation of failure process from continuum to discontinuum in geomechanics. During the crack propagation

the relative position relationships between the cracks and the mathematical meshes will be arbitrary; for example

the crack tip may locate in the interior

on the node or on the edge of the mesh. For the same crack

the mesh independency of NMM in dealing with the linear elastic crack problems is studied by rotating and moving the mathematical meshes to construct the relationships and some extreme cases that may have an influence on the results and taking stress intensity factor as the measurement. The results in this study to the NMM show it has little mesh dependency even in treating strong singularity

implying it will be robust in simulating crack propagation.