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We present an optimum design method for a rectangular reinforced concrete beam using Genetic Algorithms. The optimum design procedure in this paper employs 2 design cases: i) all of the design variables (b, d, As) of the rectangular reinforced concrete section are used pseudo-continuously, ii) one is pseudo-continuous for the concrete cross section (b, d) and the other is discrete, using an index for the steel area (As). The optimum design in this paper uses Chakrabarty's model. In this paper, the Genetic Algorithms use the method of Elitism and penalty parameters to improve the fitness in the reproduction process, which leads to very practical designs. The optimum design of the steel area in the examples uses ASTM standard reinforcing bars (#3~#11, #14, #18).