Abstract: An automatic polishing machine which can polish a curved skin of a large area fully automatically and efficiently along a three-dimensional plane of the skin. The machine comprises a fixed horizontal beam, a movable table movable in a horizontal direction perpendicular to the beam for receiving thereon a work to be polished, a carriage mounted for movement on the beam, a slider mounted for up and down movement on the carriage, a turning member mounted for forward and backward turning movement within a predetermined angular range on an arcuate rail which is located at a lower end portion of the slider and has an upwardly swollen arcuate configuration, a rocking member mounted for up and down rocking motion on the turning member, a spindle supported for rotation on the rocking member, and a buff removably mounted on the spindle.