Abstract: The invention proposes a method for grinding plastics or glass, in particular for grinding acrylic glass, where a mechanically driven grinding tool is moved across a surface to be finished (44). Grinding is effected by a dry process, without any liquid working agent, the grinding tool performing an orbital movement, or oscillating about a fixed rotary axis at high frequencies, while the grinding dust is extracted from the marginal area. The grinding tool comprises a closed abrasive with resiliently embedded abrasive grains, a plurality of the resiliently embedded abrasive grains having, preferably, level front surfaces which are delimited by relatively sharp edges at the transition to their lateral surfaces, the greatest part of the front surfaces being oriented to extend substantially in parallel to the surface to be worked (44). The method enables plastic and glass surfaces to be micro-finished to a particularly high grade (FIG. 1).