Accuracy and reliability of FEM are influenced by yielding criterion,so it is very important to choose one proper yield criterion for stability analysis when using overload numerical method. In order to investigate the essential relationship between Druker_Prager yield criterion and overload safety factor of gravity dam and further afford theoretical warrant for numerical computation, explicit expression for the relationship between the Druker_Prager yield criteria and the overload safety factor of an ideal gravity dam is established by using stress solution, and the gravity dam’s stability of Xiangjiaba hydro power project has been investigated by using FEM. Both indicate that the overload factor reaches its minimum when the inscribed cone yield criterion is used, and reaches its maximum when the expansive cone yield criterion is used.