The contact between a power-law hardening elastic–plastic sphere and a rigid flat under combined normal and tangential loads in full stick is studied in this work. The displacement-driven loading is used since the frictional contact problems under the displacement-driven loading are widespread in the fields of metal forming and orthogonal cutting. The loading process is as follows: First, a normal displacement-driven loading is imposed on the rigid flat and kept constant; then, an additional tangential displacement-driven loading is applied to the rigid flat. The elastic–plastic contact behavior in presliding is investigated with a proposed finite element (FE) model, including the tangential force, the von Mises stress, the normal force, the contact pressure, and the contact area. The effect of the strain-hardening exponent on contact behavior is considered. It is seen that the tangential force increases nonlinearly with the increase of the tangential displacement, exhibiting gradual stiffness reduction which implies that the junction becomes more plastic. The von Mises stresses moves along the direction of the tangential load, while the maximum stress moves to the contact surface from the below. The normal force diminishes as the tangential load increases, and more obviously for the lower hardening exponent cases. The contact pressure also decreases more significantly for the lower hardening exponent cases. In addition, smaller exponents result in a greater increase of the contact area. The empirical expressions of the tangential force and the contact area in the tangential loading process are also proposed by fitting to the FE results.