A novel method to determine the health of the industrial parts is using the ultrasound scattering waves. Any changes in the structure of the scattering object or in the boundary conditions will cause a change in the scattering field. The frequency spectrum of the scattering time signal has valuable information, which is studied by resonant ultrasound spectroscopy (RUS). Since any defect, property changes, or changes in boundary conditions can affect the scattering field. Therefore, the possible defects in the piece are detected using the response of the scattering field. One possible defect in the fiber-reinforced composites is the existence of a crack in the matrix or fibers. In the present study, the effect of crack on the far-field backscattering amplitude spectrum is investigated using the finite element method (FEM). To this end, the effect of the crack’s direction in the cylinder and matrix on the form function is scrutinized. The results show that the Rayleigh frequency modes are more sensitive to the cracks existing in the epoxy matrix than the Whispering-gallery frequency modes. Also, the existence of the crack in the aluminum cylinder has the most effect on the Whispering-gallery frequency modes. Besides, the existence of a horizontal crack in the aluminum cylinder leads to a significant reduction in these frequency modes. The validation of the research is determined by comparing the steel cylinder form function obtained from the finite element method’s information and the analytical and experimental form functions in addition to the comparison of the aluminum cylinder form function and reference form function.