In the field of earth science research,finite element method has long been deemed as one of the most important analysis tools.In this paper several main-stream fault-simulation approaches are summarized when international scholars conduct scientific researches in geosciences,especially in seismology and crustal geomorphology using continuum-based numerical method and finite element method,their relevant progress in geosciences are expounded.Generally speaking,the simulation models of geological faults can be categorized into four types： weak zone model,split node model,contact model,and block model.