Abstract: In a grinding apparatus with a rotor device driving an eccentrically mounted carrier device in which a shaft is mounted provided at one end with a head to which a supporting face for abrasive paper is fastened, facilitated grinding of curved surfaces by hand is obtained by the features that the supporting face is of curved design and has upper and lower sides with the same radius of curvature and is fastened to the head via an elastic element, and at least two guide devices are provided which cause the supporting face to be guided by the head reciprocatingly along a curved surface with the same radius of curvature as the supporting face.