Abstract: A rotatable drum 4 is supported by rollers 5 on a travelling frame member 1, and surrounds a pipe 3 gripped by the frame member. Swing levers 6, 6' coupled at their one ends to and driven by fluid pressure cylinders 10, 10' are pivotally mounted on the drum at journals 7, 7', and guide rollers 11, 11' and associated cutting and chamfering members 9, 9' rotatably driven by motors 8, 8' are mounted on the swing levers and extend inwardly towards the pipe. Pressure fluctuations in the cylinders are absorbed by accumulators 13, 13', whereby the chamfering and cutting members are sequentially driven into engagement with and smoothly follow the uneven contours of the pipe surface.