The incorporation of the saturation of the tangential contact stress with the increase of the normal contact stress is required for the analysis of the friction phenomenon of solids and structures subjected to a high normal contact stress, which cannot be described by the Coulomb friction condition, in which the tangential contact stress increases linearly with the increase of the normal contact stress. In this article, the subloading-friction model, which is capable of describing the smooth elastic–plastic transition, the static–kinetic transition, and the recovery of the static friction during the cease of sliding, is extended to describe this property. Further, some numerical examples are shown, and the validity of the present model will be verified by the simulation of the test data on the linear sliding of metals.