The identification, localization and evaluation of damages in structures using global analysis methods, from the point of view of the dynamic behavior of the structure, is a current topic. In this context, the paper is focused on the study of thin circular plates with damages. The natural frequencies and modal shapes of the circular plate are calculated analytically and numerically by applying the finite element method. The circular plate has a damage located at different radii from the center of the plate, the damage is considered to have the shape of an arc of a circle. The natural frequencies thus obtained constitute a database that took into account the two angular openings of the damage, of 22.50, respectively 900 and the radius at which the damage is located. With these values of natural frequencies, using artificial intelligence (AI), and the MATLAB software, the database is used to train a machine learning model that predicts the probable angular opening of the damage knowing its location from the center of the circular plate.