A wave bevelling machine is disclosed which produces a wave bevel on a glass work piece. The machine includes a feed path that is adapted to receive a glass work piece and which includes a plurality of spaced-apart treatment heads adjacent the feed path and adapted to sequentially engage the edge region of the work piece as the work piece is moved along the feed path. Each of the plurality of heads includes at least one contact region adapted to contact the edge region of the work piece, and one or more of the heads is adapted to abrade glass from the edge region when in contact with the edge region. The machine further includes a treatment head positioning system adapted to cause the contact surfaces of the plurality of heads and the edge region of the work piece to be engaged and cyclically moved in an oscillating path with respect to each other to produce the wave bevel on the edge region. The machine may further include one or more conveyors that support and move the work piece along the feed path. Furthermore the heads may be mounted on a single carriage, on which they move or are engaged as a unit, or may be independently mounted, wherein they may each be controlled and positioned by the treatment head positioning system independent of the rest of the plurality of heads.