This paper studies the optimum design problems of concrete faced rockfill dams (CFRD) on alluvial deposit with interval analysis method. Based on the structural characteristics and service conditions of CFRD, a mathematical model of optimum design is established and the interval optimum method is discussed. The case study shows that the optimum plan is reasonable, reliable and economic. It has been proved in practice that the method presented in the paper is simple and effective. This method can be extended to other optimal problems.