The fault branching phenomenon, which may heavily influence the patterns of rupture propagation in fault systems, is one of the geometric complexities of fault systems that is widely observed in nature. In this study, we investigate the effect of the branching angle on the rupture inclination and the interaction between branch planes in two-fork branching fault systems by numerical simulation and theoretical analysis based on Mohr’s circle. A friction law dependent on normal stress is used, and special attention is paid to studying how ruptures on the upper and lower branch planes affect the stress and rupture on each other separately. The results show that the two branch planes affect each other in different patterns and that the intensity of the effect changes with the branching angle. The rupture of the lower branch plane has a negative effect on the rupture of the upper branch plane in the case of a small branching angle but has almost no negative effect in the case of a large branching angle. The rupture of the upper branch plane, however, suppresses the rupture of the lower branch plane regardless of whether the branching angle is large or small.