Because of the construction condition, Anti-shears strengthen of most gravity dams is low, and horizontal forces is large. As these factors, the stability against sliding of a gravity dam should be considered in the dam design. Instability of a dam and its bases is typical catastrophic phenomenon. In this paper, the stability of a dam is researched through establishing a catastrophic model. Finally, the xiangjiaba gravity dam was introduced in as an example, and the result is in accordance with that of the finite element strength reduction method.