Knowledge of the crustal stress state is important for understanding tectonic processes and seismic hazard assessment as well as for various practical applications. In this study, we present a model describing the contemporary 3D crustal background stress field of the eastern Tibetan Plateau. The model incorporates a complex fault system and an appropriate initial stress state that matches both model-independent stress observations and kinematic data well. Our results show that the modeled maximum horizontal stress SH is generally oriented in NW-SE direction. The Bayan Har Block and the Chuan-Dian Block are dominated by a strike-slip faulting stress regime. However, in some local areas, the crust is governed by a normal faulting regime. We infer that the local normal faulting stress regime in the Bamei-Kangding area is caused by the clockwise rotation of the strike of the Xianshuihe fault at Kangding. This normal faulting stress regime would promote the ascent of intrusions and provide the space necessary for the emplacement of the Zheduoshan granite. The stress state on the Longmen Shan fault zone is rather inhomogeneous. For the Yingxiu-Beichuan fault, the northeastern segment has a lower normal stress but a higher shear stress than the southwestern segment. This inhomogeneous stress state on the Yingxiu-Beichuan fault could provide an explanation for the northeastward propagation of the ultra-long unilateral rupture in the Wenchuan Ms8.0 earthquake. According to the stress state on the Xianshuihe fault, we conclude that the Kangding-Shimian segment has a high potential to produce a strong earthquake due to its high normal stress and a fast slip rate and should be carefully monitored. On the Bamei-Kangding segment, which is governed by a normal faulting stress regime and may be lubricated by fluids, slip seems to be facilitated favoring more frequent small to moderate magnitude earthquakes to occur on this segment.