In multibody indentation problems of functionally graded materials, characteristics and gradation of material constituents are greatly influence the response of these problems. The objective of the present study is two folds. The first is to develop a comprehensive and efficient 2D nonlinear inequality constrained variational finite element model capable of analyzing multibody frictional indentation problems of FGMs considering a realistic friction model. The second fold is to investigate the effects of material properties of the constituents of functional graded materials and their gradation, coefficient of friction, and indenter size on the response of multibody frictional indentation systems. For multibody contact configuration, different types of contact at different contact interfaces are modeled in the framework of contact mechanics. To overcome the drawbacks of classical Coulomb's law of friction, friction at the indentation interfaces is modelled using the nonclassical nonlinear local friction model to realize the tangential frictional stress and relative tangential displacements. All frictional contact constraints at all contact interfaces are exactly fulfilled without any penalty parameters. The isoparametric graded finite element formulation is utilized to realize the material properties of FGMs. Application of the developed model is verified with analytical models available in the literature and very well agreement is found. A case study of an unboned elastically graded layered homogeneous elastic substrate indented by a flat rigid indenter subjected to simultaneous normal and tangential loadings is comprehensively investigated. A detailed parametric study is conducted to explore the effect of the layer gradation index, coefficient of friction, and indenter width on the indentation response, which including contact pressure, tangential frictional stress and displacement field at the indenter-graded layer interface and graded layer-elastic substrate interface. Results show that the receding frictional contact response of FGMs can be controlled by appropriate choice of the layer gradient index.