<p>In this study, the free vibrations of multiple-cracked nanostructures composed of functionally graded materials (FGMs) are investigated based on the nonlocal elastic theory (NET) and the dynamic stiffness method (DSM). The material properties of the FGMs vary nonlinearly along the height of the beam element. Cracks in the FGM nanostructures are modeled as two elastic springs connecting the intact segments at the cracked section. The differential equations of motion of a multiple-cracked FGM Timoshenko nanobeam element are derived using Hamilton’s principle and the NET with continuity conditions incorporated at the cracked sections. Exact closed-form solutions, which resolve the nonlocal paradox associated with the fundamental frequency of FGM cantilever beams, are proposed to construct the dynamic stiffness matrices for multiple-cracked FGM nanostructures under arbitrary boundary conditions. The proposed DSM model enables efficient and accurate computation of the free vibrations of multiple-cracked FGM nanostructures using a minimal number of elements. The reliability of the proposed DSM-based solutions is validated through comparisons with existing numerical results in the literature. Furthermore, the effects of the nonlocal parameters, material gradation, geometric properties, and elastic foundation on the vibration behavior of multiple-cracked FGM nanostructures are analyzed in detail.</p>