Abstract: This paper emphasized the importance of studying dynamic rupture process of earthquake source. In this study, we investigated the influences of complex fault geometry and medium, and introduced some numerical methods, such as finite element method, discrete element method, finite difference method and boundary integral equation method. We further discussed advantages and disadvantages of these methods and suggested that the choice of the methods depend on the concrete problem and calculation accuracy. Finally, we discussed the application of slip friction law to the dynamic simulation. Commonly used friction laws were slip-weakening law, slip rate-weakening law and rate-state dependent friction law. If we simply considered the dynamic rupture process of a single earthquake, slip-weakening law was more widely used, in which choosing reasonable slip weakening distance was very important. However, if we studied a whole seismic cycle, rate and state dependent friction law would be more appropriate.