This study offers the elastic response of the variable thickness functionally graded (FG) by single walled carbon nanotubes reinforced composite (CNTRC) moderately thick cylindrical panels under rotating and transverse mechanical loadings. It’s considered that, three kinds of distributions of carbon nanotubes which are uniaxial aligned in the longitudinal direction and two functionally graded in the transverse direction of the cylindrical panels. Depending on first order shear deformation theory (FSDT), the governing equations can be derived. The partial differential equations are solved by utilizing the technique of finite element method (FEM) with a program has been built by using FORTRAN 95. The results are calculated to investigate the influence of the variable thickness, geometric parameters, rotating velocity, carbon nanotubes (CNTs) volume fraction for different boundary conditions on the non-dimensional deflection of the cylindrical panels. A comparison study has been carried out between the results of present study and that available in the open literature and found very good correspondence between the two results.