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The contact problem with adhesion for a functionally graded coated half-space indented by a rigid spherical punch is considered. The whole contact region is stick assuming the interfacial friction sufficient to prevent any slip taking place between the indenter and the coated half-space. The linear multi-layered model is used to model functionally graded materials with arbitrarily varying shear modulus and constant Poisson's ratio under axisymmetric loads. By using the transfer matrix method and Hankel integral transform technique, the problem is reduced to a set of Cauchy singular integral equations. An iterative method is developed to numerically solve singular integral equations. The contact stress and indentation are calculated for different variations in elastic modulus. It is found that appropriate gradual variation in the shear modulus can improve the resistance to contact damage at the contact surfaces. [ABSTRACT FROM AUTHOR]