It is of great importance to establish the dam failure risk criteria for dam risk assessment and management. Presently, the F-N curve method is widely applied in practice, in which the F-N curves are used for establishing the criteria for separate risks caused by the dam failure in life, economy, environment, and society respectively. In this paper, in consideration of the overlying effect by two or more types of risk losses resulting from the dam failure at the same time, the F-N curved surface method is presented for establishing the integrated dam failure risk criteria. In this method, the named F-N curved surfaces are established, and by these curved surfaces, the acceptable, the allowable, and the unallowable integrated risk zones can be defined. It is of great importance to establish the dam failure risk criteria for dam risk assessment and management. Presently, the FN curve method is widely applied in practice, in which the FN curves are used for establishing the criteria for separate risks caused by the dam failure in life, economy, environment, and society respectively. In this paper, in consideration of the overlying effect by two or more types of risk losses resulting from the dam failure at the same time, the FN curved surface method is presented for establishing the integrated dam failure risk criteria. In this method, the named FN curved surfaces are established, and by these curved surfaces, the acceptable, the allowable, and the unallowable integrated risk zones can be defined.