This paper studies the dam foundation stability of the representative no. 3 powerhouse-dam section of the Three Gorges Dam (TGD), China, using elastic-plastic finite element shear strength reduction technique. In the no. 3 powerhouse-dam section area, the low-angle discontinuities, such as joints and faults, are mostly developed in the dam foundation rock mass, and constitute deep foundation stability problems. These weak structure planes affecting the dam foundation stability are modeled as continuum bodies in the finite element modeling according to their respective spatial geometrical characteristics including inclination and dip angle. Three-dimensional elastic-plastic finite element analyses are performed to obtain the stress and deformation distributions of TGD foundation and concrete structures. The factor of safety (FOS) of TGD foundation stability against sliding and its failure mechanics are comprehensively evaluated with the following criteria: (a) The maximum of the trial factors of shear strength reduction can be reached by which the dam foundation is brought to the critical equilibrium state; (b) The inflection points of the curves of the displacements of dam heel, dam toe and dam top, vs. the trial factors of shear strength reduction are located; and (c) Plastic zones develop along the potential sliding paths consisting of the dam heel, long and large joints, and other weak structure planes as the trial factors increase. The results obtained show that the dam foundation of the no. 3 powerhouse-dam section is stable under the designed normal load combinations. The evaluations of the FOS of dam foundation stability presented may provide a significant reference for the safety assessment of TGD in the Three Gorges Project, China.