To provide a device for and a method of polishing a flange surface of a quartz glass-made tube with flange like a quartz glass-made outer tube which can perform lap polishing of the flange surface in a step of the end of manufacture (condition after outer tube with flange).

This polishing device for a flange surface of a quartz glass-made outer tube for mirror polishing the flange surface 3a of a flange 3 mounted in a pipe barrel end part of the quartz glass-made outer tube 1, comprises a hold rotational mechanism 4 for holding a pipe barrel part 2 capable of rotating of the outer tube 1 and a polishing mechanism 5 for mirror polishing the flange surface 3a of the flange 3 mounted in the pipe barrel end part of the outer tube 1 by a polishing pad 5b mounted in the tip end part of an air spindle 5a through an elastic member 5c.