A computational model is developed for the analysis of elastic and partially plastic stress states in functionally graded (FGM) variable thickness rotating solid disks. The modulus of elasticity, Poisson's ratio, uniaxial yield limit and density of the disk material are assumed to vary radially in any prescribed functional forms. Small deformations and a state of plane stress are presumed. Using the von Mises yield criterion, total deformation theory and a Swift-type nonlinear hardening law, a single nonlinear equation describing elastoplastic behavior of rotating disk is obtained. A shooting technique using Newton iterations with numerically approximated tangents is designed and used for the computer solution of the governing equation. The model is verified by comparing predictions with analytical solutions.