A problem of quasi-static growth of an arbitrary shaped-crack along an interface requires many times of iterations not only for finding a spatial distribution of discontinuity but also for determining the crack tip. This is crucial when refining model resolution and also when the phenomena progresses quickly from one step to another. We propose a mathematical reformu-lation of the problem as a nonlinear equation and adopt different numerical methods to solve it efficiently. Compared to a previous work of the authors, the resulting code shows a great improvement of performance. This gain is important for further application of aseismic slip process along the fault interface, in the context of plate convergence as well as the reactivation of fault systems in reservoirs.