PURPOSE: To provide a cylinder for a rotary positive displacement machine which does not require polishing balls, a process for producing the same and the rotary positive displacement machine using the cylinder.

CONSTITUTION: The cylinder 6 is produced by rolling a sheet metal blank 1 to form a cylindrical tube. The blank 1 includes a polished surface 2 which forms the inner surface of the cylindrical tube, a pair of opposite parallel edges 3 which are normal to the axis of the cylindrical tube, and a pair of opposite edges to each other 4 which form a slot 7. The slot 7 intersects the tube ends and extends obliquely to the tube axis over at least a major part of the length of the tube. The cylinder 6 is mounted in an elastically compressed state in a bore in a casing of the rotary positive displacement machine having a vaned rotor. The slot 7 may be freely opened and closed, to serve as an inlet or exhaust opening at the time of opening.