Over the last three decades, researchers have responded to the demands of industry to manufacture mechanical components with geometrical tolerance, dimensional tolerance, and surface finishing in nanometer levels. The new lapgrinding process developed in Brazil utilizes lapping kinematics and a flat grinding wheel dressed with a single-point diamond dresser in agreement with overlap factor (Ud) theory. In the present work, the influences of different Ud values on dressing (Ud = 1, 3 e 5) and grain size of the grinding wheel made of silicon carbide (SiC = 800, 600 e 300 mesh) are analyzed on surface finishing of stainless steel AISI 420 flat workpieces submitted to the lapgrinding process. The best results, obtained after 10 minutes of machining, were: average surface roughness (Ra) 1.92 nm; 1.19 µm flatness deviation of 25.4 mm diameter workpieces and mirrored surface finishing. Given the surface quality achieved, the lapgrinding process can be included among the ultra-precision finishing processes and, depending on the application, the steps of lapping followed by polishing can be replaced by the proposed abrasive process.