In this study, optimal design of two-dimensional functionally graded thick flywheels is obtained by the generalized differential quadrature method (GDQM) and the non-dominated sorting genetic algorithm II (NSGA II). The flywheel cross section is parameterized with the Bezier surface, and a mapping procedure to discretize non-rectangular solution domain by the GDQM is introduced. The results of this novel technique are compared with the results available in open literature and the ANSYS finite element solution, and a very good agreement is observed. Pareto optimal solutions for minimum mass and maximum energy storage capability are obtained for two types of bearing, one being mechanical and the other magnetic. Consequently, the optimal cross-section geometry and the two-dimensional material distribution of functionally graded (FG) flywheel are obtained.