It is pointed out that there exists a vast amount of fuzzy information in both objective and constraint functions of optimum design of structures (ODS) Thus, relatively reasonable optimum designs can only be obtained by fuzzy programming methods. While all fuzzy constraints enclose a fuzzy feasible region in decision-making space, the fuzzy optimum solution will be a sequence of points in a small fuzzy optimum subregion. In the presented procedure, optimum structural design with fuzzy constraints is transformed into a set of ordinary optimum problems by a level cuts approach which results in a sequence of optimum design schemes with different design levels. The concept of optimum design level corresponding to the most suitable scheme among the obtained sequence is also advanced in this paper.