The method consists in flanging the wall of a thick-walled shell around a hole made in said wall in adavance until a branch pipe is produced, in calibrating said shell on the inside surface adjoining the branch pipe, and simultaneous straightening of the thick-walled shell on its outside surface in the direction of the longitudinal axis of the branch pipe from the side opposite to the location of said branch pipe.The device for the realization of the method according to the invention comprises a flanging die with guide columns secured on it, said columns carrying a cantilevered arbor capable of moving longitudinally and provided with a mechanism for fixing it in the initial position, and pushers fastened on the movable cross-head of a press, and arranged normally to the longitudinal axis of the arbor with which they interact and symmetrically to the longitudinal axis of the flanging punch and there is an additional die located between said pushers, the lower surface of said additional die having a shape corresponding to the shape of the outer surface of the shell while the lower surface of the punch holder has a shape corresponding to the shape of the inside surface of the shell. Besides, the flanging die is provided with projections entering the slots on the faces of the thick-walled shell.