Material tailoring in functionally graded isotropic hollow rods of arbitrary cross section under torsion is studied. The purposes of material tailoring pursued in this paper are divided into two categories. In the first category, we find the variation of the volume fractions of constituents of a functionally graded member under torsion to obtain an appropriate distribution of shear stress over the cross section. In the second category, the torsional rigidity of a rod with a pre-defined mass is maximized by appropriate determination of the variation of constituents of the functionally graded material. Hollow rods are studied in this paper since they have higher torsional rigidity compared to solid members with the same mass. Meshless numerical methods are used for torsional analysis of the cross sections. Moreover, numerical optimization methods are used for material tailoring of the rods. Several examples with different cross sections are presented to investigate the usefulness of the proposed technique on achieving the mentioned purposes.