This paper deals with the optimum cost design of partially prestressed concrete I crosssectioned beams by using Genetic Algorithms. For this purpose, the optimum cost design of two selected example problems that have different characteristics in behavior are performed via Genetic Algorithms by determining their objective functions, design variables and constraints. The results obtained from the technical literature are compared with the ones obtained from this study. The interpretation of the results show that the design of partially prestressed concrete I crossectioned beams from cost point of view by using Genetic Algorithms is 35 similar to 50 % more economical than the traditional ones (technical literature) without conceding safety.