This paper presents an analytical method developed to investigate the dynamic frictional contact mechanics between a functionally graded coating and a rigid moving cylindrical punch. Governing partial differential equations of elastodynamics are solved analytically by applying Galilean and Fourier transformations. Interface continuity and boundary conditions are written and contact problem is then reduced to a singular integral equation of the second kind. The singular integral equation is solved numerically by means of an expansion-collocation method. Developed solution procedures are verified through the comparisons made to the results available in the literature. Presented parametric analyses illustrate the effects of punch speed, coefficient of friction, material inhomogeneity and geometric parameters upon the contact stresses. It is shown that, especially at higher punch speeds, the difference between contact stresses obtained through elastodynamic and elastostatic solutions is rather significant. A formulation based on the elastodynamic theory, as presented in the current study, is required to compute more realistic contact stresses. (C) 2018 Elsevier Ltd. All rights reserved.