<p>Spherical contact under combined normal and cyclic tangential loading is a simple but representative issue in contact mechanics. This work developed a generalized three-phase constitutive model considering elastic, yield plateau, and strain hardening characteristics and contributed an energy conservation model of quasi-static contact under various sliding conditions. The von Mises stress, equivalent plastic strain, contact behaviors, and energy components were examined under different material parameters and loading conditions. The results indicate that the stress concentration zone appears in the heading area of the sliding direction and vanishes in the trailing area; junction growth derives from a new increased zone and an accumulated plastic deformation inside the original contact zone; large normal force decrement, substantial junction growth, and considerable energy dissipation occur in the material more prone to higher plastic deformations; there are more complex responses related to single frictional dissipation and plastic dissipation.</p>