Free vibration analysis of thick functionally graded nanocomposite annular and solid disks with variable thickness reinforced by single-walled carbon nanotubes (SWCNTs) is presented. Four types of distribution of uniaxial aligned SWCNTs are considered: uniform and three kinds of functionally graded (FG) distribution through radial direction of the disk. The effective material properties of the nanocomposite disk are estimated by a micro mechanical model. The axisymmetric conditions are assumed and employing the graded finite element method (GFEM), the equations are solved. The solution is considered for four different thickness profiles, namely constant, linear, concave and convex. The achieved results show that the type of distribution and volume fraction of CNTs and thickness profile have a great effect on normalized natural frequencies.