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Shallow foundations are commonly used for low-rise buildings. The column axial loads and moments are transmitted to the soil through a reinforced concrete pad. The size of the pad as an isolated footing depends on the bearing capacity as well as the base column loading. In this paper, the bearing capacity of the soil is taken from Terzaghi formula so that designing the size of the footing is not straightforward. This is because the soil bearing capacity depends on the soil properties, and the depth and width of the footing. Therefore, the soil bearing capacity and the width of the footing should be obtained iteratively. This condition is coupled with the thickness and reinforcement of the concrete footing to resist shear and bending moment and to attain the optimum design. To solve the problem and to obtain an optimum design, a genetic algorithm (GA) is used. The objective is to design a square concrete footing to minimize the cost of the foundation. Two cases are considered in this paper. The first case is when the depth of footing is decided before hand by the designer. In this case only the width of the pad, the thickness of the concrete, and the amount of the reinforcement have to be obtained. The second case is when the width of the pad, the thickness of the concrete, and the amount of the reinforcement as well as the depth of the footing should be obtained as the design variables. For both cases the optimum design can be achieved by using genetic algorithms.