Roughness of curved surfaces finished with flexible tools depends on the tool/work contact pressure and area. In this study, non-Hertzian closely conforming elastic contact theory is employed to analyze the tool/work contact and to generate a tool path producing a constant pressure at initial contact points. Finishing experiments on curved surfaced are conducted using the tool path. For comparison, curved surface finishing is also performed along the tool path producing a constant tool/work interference depth. It is demonstrated that the tool path of constant contact pressure improves the finished surface roughness.