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The author offers a systematic and careful development of many aspects of structural optimization, particularly for beams and plates. Some of the results are new and some have appeared only in specialized Soviet journals, or as pro- ceedings of conferences, and are not easily accessible to Western engineers and mathematicians. Some aspects of the theory presented here, such as optimiza- tion of anisotropic properties of elastic structural elements, have not been con- sidered to any extent by Western research engineers. The author's treatment is "classical", i.e., employing classical analysis. Classical calculus of variations, the complex variables approach, and the Kolosov- Muskhelishvili theory are the basic techniques used. He derives many results that are of interest to practical structural engineers, such as optimum designs of structural elements submerged in a flowing fluid (which is of obvious interest in aircraft design, in ship building, in designing turbines, etc.). Optimization with incomplete information concerning the loads (which is the case in a great majority of practical design considerations) is treated thoroughly. For example, one can only estimate the weight of the traffic on a bridge, the wind load, the additional loads if a river floods, or possible earthquake loads.