The adhesive frictional contact under shear load is analyzed for axisymmetric power-law graded elastic bodies, in the framework of the MaugisMaugis model of adhesion and the CattaneoCattaneo approximation of frictional contact. Mode-mixing and surface roughnessRoughness are neglected. The known adhesive normal contact solution is revisited by considering the contact as a series of incremental rigid flat punch translations. The tangential contact problem is solved under the assumption that the physical compressive stress between surface points—consisting of the contact pressure and the adhesive attraction—can serve as the basis for a Amontons-Coulomb lawAmontons-Coulomb law for the frictional tractions. Thereby, the tangential problem with friction is reduced to the corresponding (frictionless) indentation problem. Parabolic contact, and the influences of material grading and adhesion range on the contact solution are studied in detail.