A method for manufacturing a tube with varying external diameters by reducing a shell formed into a tube over a mandrel in a cold pilger rolling mill, which shell is worked between a set of driven ring rolls each having at least two different cooperative varying diameter tube producing grooves formed circumferentially around the periphery of said rolls, and each groove having a reducing range including a rotating and feeding zone, and a smoothing zone, the steps comprising:
- (1) rolling a selected length of said shell in a first said groove to produce a desired first external diameter for said tube,
- (2) rotating said rolls to bring a said second groove into operation for a continued working of said shell,
- (3) rolling a selected length of said shell with said second groove to produce a second desired external diameter for said tube different than said first diameter,
- said rolling in steps (1) and (3) being such as to subject said formed tube to said smoothing zones to effect final processing of said external diameters, and
- (4) when said tube is in said first and second grooves rotating and selectively feeding said shell in said rotating and feeding zones.