An optimization method using Kriging approximation is applied to a structural optimization problem. The method involves two main processes. The first is a space estimation process that uses the Kriging method, and the second is an optimization process. The use of the Kriging method makes it easier to perform the approximation optimization. As an example of the estimation performed as part of structural optimization, a response surface for layout optimization of beam reinforcement is estimated. To evaluate the applicability of the Kriging method, Kriging estimation is compared with neural network approximation. As a numerical example, the optimization of a stiffened cylinder for an eigenfrequency problem is illustrated. The obtained results clearly show the applicability of the method.