A body insonified by a sound field is known to experience a steady force that is called the acoustic radiation force. In this paper, the method of wave function expansion is adopted to study the scattering and the radiation force function caused by a plane normal harmonic acoustic wave incident upon an arbitrarily thick-walled functionally graded cylindrical shell submerged in and filled with compressible ideal fluids. A laminate approximate model and the so-called state space formulation in conjunction with the classical transfer matrix (T-matrix) approach are employed to present an analytical solution based on the two-dimensional exact equations of elasticity. Two typical models, representing the elastic properties of FGM interlayer, are considered. In both models, the mechanical properties of the graded shell are assumed to vary smoothly and continuously with the change of volume concentrations of the constituting materials across the thickness of the shell. In the first model, the simple rule of mixture governs. In the second, an elegant self-consistent micromechanical model which assumes an interconnected skeletal microstructure in the graded region is employed. Particular attention is paid on dynamical response of these models in a wide range of frequency and for different shell wall-thicknesses. In continue, by focusing on the second model, the normalized radiation force function and the form function amplitude are calculated and compared for different shell wall thicknesses and various profile of variations. Limiting cases are considered and good agreements with the solutions available in the literature are obtained.