A three-dimensional elasticity solution for the analysis of functionally graded rotating cylinders with variable thickness profile is proposed. The axisymmetric structure has been divided in several divisions in the radial direction. Constant mechanical properties and thickness profile are assumed within each division. The solution is considered for four different thickness profiles, namely constant, linear, concave, and convex. It is shown that the linear, concave, and convex thickness profiles have smaller stress values compared to a constant thickness profile. The effects of various grading indices as well as different boundary conditions, namely solid, free–free hollow and fixed–free hollow structures are discussed. A series of numerical results using zirconia as outer surface ceramic and aluminium as inner surface metal are presented. Parametric study has then been carried out to give a better understanding of how different stress, strain, and displacement components change along radial and axial directions of the rotating structures. Numerical results show that for a given grading index, the structures with a concave thickness profile have the smaller circumferential strain and stress compared to other thickness profiles.