Stress field in functionally graded (FG) rotating disks with non-uniform thickness and variable angular velocity is studied numerically. The elastic modulus and mass density of the disks are assumed to be varying along the radius as a power-law function of the radial coordinate, while the Poisson's ratio is kept constant. The governing equations for the stress field is derived and numerically solved using the finite difference method for the case of fixed-free boundary conditions. Additionally, the effect of material gradient index (i.e., the level of material gradation) on the stress field is evaluated. Our results show that the optimum stress field is achieved by having a thickness profile in the form of a rational function of the radial coordinate. Moreover, a smaller stress field can be developed by having greater mass density and elastic modulus at the outer radius of the disk (i.e., ceramic-rich composites at the outer radius). The numerical results additionally reveal that deceleration results in shear-stress development within the disks where a greater deceleration leads to greater shear stress; however this has almost no effect on the radial and circumferential stresses. Furthermore, the shear stress can cause a shift in the location of the maximum Von Mises stress, where for small deceleration, maximum Von Mises stress is located somewhere between the inner and outer radii, while for large deceleration it is located at the inner radius.