Knowing the eigenfrequencies of a space is important for designing its acoustic performance at low frequencies. The eigenfrequencies can be analytically calculated for a limited set of room shapes, while for more complex domains it is common to use Finite Element methods (FEM). This paper investigates the use of Convolutional Neural Networks (CNN) to predict the eigenfrequencies based on a digital image of a 2D room shape. FEM software is used to create a training set of pseudorandom room shapes and identify their eigenfrequencies. In this study, only rooms with rigid walls are studied, and the CNN is used to predict the first ten eigenfrequencies for rooms with normalized surface area. The rooms have three to sixteen walls, including slanted walls and non-convex geometries, as well as corridor rooms. The accuracy of this approach is compared to the FEM solutions, as well as to analytical solutions for room shapes with solutions available.