In this paper, a method for identifying of a crack in a plate that uses a genetic algorithm (GA) based on changes in natural frequencies is presented. To calculate the natural frequencies of the cracked plates, a FEM (Finite Element Method) program, which is based on the BFM (Bogner, Fox and Schmidt) model, is developed since the accuracy of the forward solver is important. In the analysis, two types of cracks, i.e., internal and edge cracks are considered. To identify the crack location and the depth from frequency measurements, the width and position of the crack in a plate are coded into a fixed-length binary digit string. Using GA, the square sum of residuals between the measured data and the calculated data is minimized in the identification process and thus the crack is identified. To avoid a high calculation cost, the response surface method (RSM) is also adopted in the minimizing process. The combination of GA and RSM makes the identification more effective and robust. The applicability of the proposed method is confirmed by the results of numerical simulation.