The results of computational experiments for determining the effect of a mode I surface fatigue crack cross-sectional shape in a rectangular cantilever beam on the characteristics of its free and forced bending vibrations with varying cross-sectional dimensions of the crack and its longitudinal position are presented. Finite-element models of beams with 8-node 3D finite elements were developed for carrying out investigations. Three types of a breathing crack cross-section were considered: rectangular, triangular, and trapezoidal one, with the solution of a contact problem to ensure the non-penetration of crack edges. Plots of relative change in the natural frequency of vibration, the amplitudes of the first and second harmonics and their ratios at the main, super- and subharmonic resonances versus the shape, relative area and location of the crack were obtained. It is shown that when bending vibrations of the beam with a rectangular crack, are excited along the axis Oy, there arise displacements only in the direction of driving force, while in the case of triangular and trapezoidal cracks, there arise additional displacements along the axis of minimum stiffness, Oz. It was found that the change in the natural frequency of the beam, as well as the ratio of the amplitudes of dominant harmonics during the recording of vibrations along the excitation axis at the main, super- and subharmonic resonances increase with increasing relative area of the crack cross-section. Under this condition, their largest value was characteristic of a rectangular crack, and the smallest of a triangular one. It was noted that a characteristic indicator of the asymmetric shape of the crack was the appearance of vibrations in the plane perpendicular to the excitation plane.