In this paper, the complex phenomena of the elastic and elastoplastic indentation responses of functionally graded materials (FGMs) are studied in the framework of frictional contact mechanics using finite element method. The proposed model accounts for the continuous gradation of all the elastic and plastic properties of the indented material along its thickness using power law function and Tamura, Tomota and Ozawa (TTO) model. Classical Coulomb's friction law is utilized to model the friction effect throughout the contact interface. The model is implemented in ANSYS FE software and utilized to simulate the axisymmetric frictional contact of an FGM substrate and a rigid spherical indenter. Parametric studies are performed to investigate the effects of friction coefficient, gradient index, and FGM-constituent materials on the frictional indentation behaviors of elastic and elastoplastic FGMs under loading/unloading pattern. Results show that the frictional contact response of elastoplastic FGMs can be controlled by appropriate choice of the gradient index. Using obtained numerical results, an empirical equation is derived to predict the normalized residual indentation depth for elastoplastic FGMs by knowing the gradient index and a single material parameter under frictional spherical indentation.