The free vibrations of rectangular FGM plates with through internal cracks are investigated using the Ritz method. Three-dimensional elasticity theory is employed, and new sets of admissible functions for the displacement fields are proposed to enhance the effectiveness of the Ritz method in modeling the behaviors of cracked plates. The proposed admissible functions accurately describe the stress singularities at the fronts of the crack and display displacement discontinuities across the crack. The correctness and validity of the present approach are established through comprehensive convergence studies and comparisons with published results for homogeneous cracked plates, based on various plate theories. The locally effective material properties of FGM in the thickness direction are estimated by a simple power law. The effects of the volume fraction of the constituents of FGM and the thickness-to-length ratio on the frequencies are investigated. Frequency data for FGM square plates with three types of boundary conditions along the four side faces and with internal cracks of various crack lengths, positions and orientations are tabulated for the first time.