Abstract: We use curvilinear grid finite difference method (FDM) to study 3-D rupture dynamics of dipping faults. By generating boundary conforming curvilinear grids based on fault plane and using coordinate transformation, physical space with curvilinear grids can be mapped to computational space with uniform orthogonal grids, so FDM can be implemented on complex surfaces. In order to verify the validity and accuracy of this method, we model self similar and spontaneous rupture of earthquake faults and compare our results with previously published ones, and find them well fitted. We focus on discussing rupture dynamics of the faults with different dip angles. We are expected to do further research on arbitrarily ldquo;non-planarrdquo; rupture dynamics in heterogeneous media and under arbitrarily curved surface using this method.