<p>This paper intends to explore the effects of cracks characteristics on free vibration behavior of functionally graded plates and shells by means of Lagrangian formulation in conjunction with the variational principle on the basis of three-dimensional theory of elasticity. The discretization of the equation of motion is achieved by using a four-noded 3D tetrahedral finite element taking into account the normal component of the displacement field in the thickness direction. The material properties of the plates and shells are assumed to vary continuously and smoothly in the thickness direction according to a general four-parameter power-law distributions in terms of volume fractions of the constituents. The consistency and reliability of the present formulation is demonstrated through several numerical tests, by comparing the obtained natural frequencies with the existing results from the literature. Three numerical examples, including the vibrational response of functionally graded rectangular and annular plates, as well as, cylindrical shells under different crack positions, orientations and lengths are studied and presented. Parametric studies on crack characteristics, geometric and material parameters are explored in deep. It was demonstrated that the crack orientation, length and positions, additionally to material characteristics of FGM structures have a significant impact on vibrational behavior of cracked FGM plates and shells, which must be considered in the structural design and performance of functionally graded plates and shells.</p>