The influence of the 2015 Gorkha earthquake on the co- and postseismic Coulomb Failure Stress (CFS) of faults in Southern Tibet is a scientific issue that warrants further investigation. We employ the flat-ramp fault slip model to calculate the Delta CFS of nearly north-south-trending rifts and east-west-trending faults in Southern Tibet. This analysis considers the Mw7.8 main-shock, the Mw7.3 aftershock, afterslip, and viscoelastic relaxation, utilizing the Burgers rheological model. By integrating the postseismic deformation and b-value, we discuss the differences and similarities in Delta CFS and the underlying mechanisms. The mainshock, aftershocks, and afterslip exhibit similar patterns of CFS effects, all acting as CFS triggers on the rifts. Viscoelastic relaxation has an unloading effect on the southern portion of the rifts, while it exerts a triggering effect on rifts located farther from the focal area, with the exception of the Dangreyongcuo rift. The influence of CFS on nearly east-west-trending faults is associated with their kinematic characteristics. Coseismic CFS triggering is concentrated in the near-source sections of the normal faults, with viscoelastic relaxation primarily resulting in unloading. The dextral strike-slip faults are governed by shear stress; the eastern sections serve as co- and postseismic CFS triggering areas, while the western sections are characterized as CFS shadow regions. Earthquakes along the Shenzha-Dingjie rift were primarily triggered by co- and postseismic CFS induced by the Gorkha earthquake. In contrast, earthquakes along the Xietongmen rift were mainly associated with elevated stress levels on the fault prior to the earthquake.