The use of multilateral wells is an important method to effectively develop complex oil reservoirs, and wellbore stability research of multilateral wells is of great importance. In the present study, the effects of formation fluids and rock damage were not taken into account by the wellbore stability model. Therefore, finite element analysis (FEA) software was used to establish a three-dimensional (3D) seepage-stress FEA model for the multilateral junctions. The model was used to analyze the wellbore stability of multilateral wells and study influences of wellbore parameters and drilling fluid density on wellbore stability at multilateral junctions. Simulation results show that the wellbore diameter insignificantly affects wellbore stability. When the angle between the main wellbore and branches enlarges to 45°, the equivalent plastic strain decreases by 0.0726, and the wellbores become more stable; when the angle is larger than or equal to 45°, the region prone to wellbore instability transfers from the multilateral junctions to the inner of multilateral wellbores. When the azimuth of wellbores is along the direction of the minimum horizontal principal stress, the equivalent plastic strain decreases by 78.2% and the wellbores are most stable. Moreover, appropriately increasing the drilling fluid density can effectively reduce the risk of wellbore instability at the multilateral junctions. A model has been developed that allows analysis of multilateral wellbore stability under seepage-stress coupling condition.