For the first time, to the authors' knowledge, the problem of the free vibration of functionally graded carbon nanotube (FG-CNT) reinforced composite moderately thick rectangular plates with edges elastically restrained against transverse displacements and rotation of the plate cross section is considered. The element-free improved moving least-squares Ritz (IMLS-Ritz) method is employed for the analysis. The first-order shear deformation theory (FSDT), accounting for transverse shear strains and rotary inertia, is used in the theoretical formulation. The applicability of the formulation is illustrated by solving a selection of example problems. The numerical results are validated through comparison and convergence studies. The effect of elastically restrained edges on the vibration behavior of the FG-CNT reinforced composite plates is studied by taking into account the CNT volume fraction ratio, CNT distribution, plate thickness-to-width ratio and plate aspect ratio. •Free vibration of CNT reinforced functionally graded plates is considered.•Plate edges are elastically restrained against translation and rotation.•The element-free IMLS-Ritz method is employed for the analysis.•The effect CNT distribution on the vibration behavior is examined.