A novel method for the numerical computation of the nonlinear normal modes (NNMs) of a highly flexible cantilever beam is presented. The flexible cantilever is modeled using a 2D finite element discretization of the geometrically exact beam model, wherein geometric nonlinearities relating to the rotation are kept entirely intact. The model is then solved using the proposed solution method, which is fully frequency domain-based and involves a novel combination of a harmonic balance (HBM) Fourier expansion with asymptotic numerical (ANM) continuation for periodic solutions. The NNMs are also calculated experimentally using a flexible cantilever specimen mounted to a shaker table. The experimental NNMs can be compared to their numerical counterparts in order to validate the frequency domain numerical technique.