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This paper describes the optimization of the beam stiffeners attached to plates in an eigenfrequency problem. The solution space is estimated using the Kriging method. A finite element analysis is carried out to evaluate the objective function at the sample points used for the estimation. The gradient method is used as a local optimizer. The Kriging estimation incurs relatively low cost, and is easy to combine with the gradient method. In this paper, we solve eigenfrequency optimization problems for a fully supported plate to maximize the minimum eigenfrequency and the difference between the 1st- and 2nd-order eigenfrequency. An optimization problem for an L-shaped plate with an eigenfrequency constraint is also solved. Good solutions are obtained for each example, and all the optimizations for these problems can be done at a lower computational cost. The results highlight the effectiveness of the method to solve the eigenfrequency optimization problems for the stiffened plate. [ABSTRACT FROM AUTHOR]