Finite element based analysis of full-stick contact between a functionally graded hemispherical asperity and a rigid flat is carried out under tangential loading. In the adopted gradation model, Young’s modulus and tangent modulus (considering bilinear isotropic hardening model) are varied according to an exponential function in the radial direction of the hemisphere. Under post-flattening tangential loading, the FGM hemispherical asperity contact is investigated for different values of gradation parameters. Different aspects of contact behavior, i.e., tangential and normal contact forces, contact area, contact pressure, etc. are investigated under the influence of varying gradation parameters. The evolution of stresses and deformation in the asperity are also studied for different gradation parameters.