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Structural optimization has become a widely used tool for various applications due to its capability of providing design freedom and promise to efficient structures. Current optimization methods are usually utilized for producing optimal structural systems subjected to design constraints under definite static or dynamic load distributions. However, engineering structures may experience randomly fluctuating loads in different physical environments. In this paper, a methodology of structural optimization with constraints on peak system responses to temporally correlated quasi-static load processes is developed. The proposed methodology provides an algorithm for generating structures of the optimal designs with constraints on their extreme responses to such environmental load sequences which have correlation features in the time domain. The computational results confirm that material distributions of optimized structures with peak response constraints highly depend on correlation levels of quasi-static load distributions under stationary processes. Furthermore, conventional optimization of structures in statics with displacement constraints is also compared with the reported optimum material distributions with peak response constraints under correlated load sequences. In consequence, the developed methodology provides a powerful tool of structural designs under stationary processes of temporally correlated loads having very low frequencies for fundamental engineering structures and further multidisciplinary mechanics researches. [ABSTRACT FROM AUTHOR]