Abstract: A new reliability analysis technique based on evidence theory that can effciently reduce the computational cost is developed for uncertain structures. In this method, a design optimization is introduced to obtain the non-probability index and a design point, and an assistant area is constructed. Through the assistant area, it can markedly reduce the number of focal elements with extreme analysis. Moreover, the computation number of the limit-state function decreases with the help of interval analysis method. Numerical examples and engineering problems are used to demonstrate the effectiveness of the proposed method.