In this report, free vibration and buckling behavior of functionally graded carbon nanotube (FG-CNT) reinforced composite thick skew and quadrilateral plates are studied. The element-free IMLS-Ritz method is used to obtain the free vibration and buckling solutions. The first-order shear deformation theory (FSDT) is employed for formulation of the energy functional to incorporate the effects of transverse shear deformation and rotary inertia. Using the IMLS approximation in the field variables and minimizing the energy functional via the Ritz procedure, a discretized eigenvalue equation of the problem is derived. The free vibration and buckling solutions can be obtained through solving this eigenvalue problem. The numerical stability of the IMLS-Ritz method is validated through convergence studies. The accuracy of the IMLS-Ritz results is examined by comparing with the known solutions. Close agreement is found from the comparison study. Besides, parametric studies are conducted for various types of CNTs distributions, CNT ratios, aspect ratios, plate geometries and thickness-to-height ratios under different boundary conditions.