The safety of concrete gravity dams as massive structures is very important issue. In complex situations, the stability analysis of concrete gravity dams is not possible by conventional software, so should other methods be used. In this study, taking into account various parameters in the dam and foundation contact, the factor of safety using the finite elements with strength reduction method is determined. In this method, the strength parameters are reduced until the instability starts. By this method the sliding stability of three different dams has been investigated. In the first model the geometry of the dam-foundation contact is horizontal; the second has unconventional contact geometry. In the third model there are two instability mechanisms. In this case, dam can slide on the horizontal surface of the contact or the instability can occur in the foundation beneath the dam. It should be noted that the stability of the last two models cannot evaluate by the conventional stability analysis. However, using the proposed method their stability safety factors can be accurately determined.