In this study, the performance of surface texturing on nonflat surfaces is numerically investigated. A one-dimensional mixed-lubrication model considering the oil supply is employed. The cases of the nonflat ring lubrication with full and partial texturing are conducted in steady-state and engine-like conditions. By considering the oil transport for lubricant distribution along the liner, the simulation for the whole ring pack is also conducted. As a main conclusion, the textured surface can obtain a special benefit on the tribological properties under not only the mixed lubrication, but also starved lubrication. In addition, it also suggests that the reduction of the ring-pack friction is possible if the nonflat top compression ring is textured.