The final stage of grinding concrete surfaces is performed by floaters with solid grinding discs. The working element in the shape of a solid wheel uses the full surface of the disc, ensuring maximum geometrical effectiveness. The disc moves in a steady progressive manner, while at the same time, rotating around its center axis. The contact line length of the full disc with the machined surface is set by geometrical effectiveness Sg. After one cycle of machining the surface with the full disc, the geometrical effectiveness measured at points on a line in a perpendicular direction from the disc moving direction has a local minimum within the machining area and zero values on the edges and outside of the machined area. Decreasing the unfavorable impact of local minimum effectiveness inside the central machining area for the uniformity of machining can be achieved by using discs with concentric working elements – rings and wheel with correctly selected sizes and rotation speeds. For increasing the machining uniformity at the edges of the machined area, partial overlap of machining zones is used in the following cycles. The article describes a disc in a threeelement system consisting of a wheel, and two rings used for optimizing uniformity of machining concrete surfaces.