© 2020 Taylor & Francis Group, LLC.Geometrically nonlinear and elastoplastic behavior of a circular FGM (functionally graded material) plate under mechanical loading–unloading condition is investigated employing three-dimensional finite element method (FEM) modeling. The through-thickness material distribution of the FGM plate is defined by a power-law variation. The elastic mechanical properties and the elastoplastic material behavior of the FGM plate described respectively by the Mori–Tanaka scheme and the TTO (Tamura–Tomota–Ozawa) model are implemented in the FEM model. The FEM model is validated presenting a very good agreement with the studies from the literature. The influences of nonlinearity, especially the elastoplastic and elastoplastic with geometrically nonlinear behavior, load parameter and thickness-to-radius ratio in terms of nonlinearity, and material composition on the mechanical behavior of the FGM plate are examined. The FEM results are evaluated in terms of the permanent central deflection and the plastic equivalent stress distributions of the FGM plate. The results indicate that a considerable difference occurs between the elastoplastic and elastoplastic with geometrically nonlinear behavior of the FGM plate in terms of both the permanent central deflection and the plastic equivalent stress distributions except ceramic-rich composition that has almost a linear–elastic material behavior, and the geometrical nonlinearity becomes an important parameter with increasing load parameter and decreasing thickness-to-radius ratio. The combination of geometrical and material nonlinearities exhibits a significant influence on the nonlinear mechanical behavior of the FGM plate under plastic deformation.