<p>The results of a numerical investigation of the delamination damage with a transverse crack on the characteristics of flexural vibrations of a cantilever composite beam at the main, superharmonic resonance of the 1/2th order and subharmonic resonance of the 2nd order are presented. For calculations, three-dimensional finite element models of beams were created in which the delamination and crack are modeled in the form of a mathematical section, and the mutual non- penetration of the damage surfaces is ensured by solving the contact problem. Numerical dependences of the influence of the delamination and crack parameters (sizes and location) on the variation of the natural frequency of flexural vibrations and on the ratio of the amplitudes of the dominant harmonics of vibrations at super- and subharmonic resonances were obtained. It was found that the presence of damage, such as delamination with a crack, has practically no effect on the natural frequency of vibrations of the composite beam. At the same time, the ratio of the amplitudes of the dominant harmonics at nonlinear resonances is sensitive to such damage.</p>