The invention relates to a method and a device for manufacturing T-pieces from an unbranched starting piece of pipe by means of internal high-pressure forming (IHF). For this purpose, the starting piece of pipe is placed in a two-part forming tool which gives the shape, can be opened and closed, surrounds the starting piece of pipe, and has a cutout corresponding to the desired shape of the T-shaped pipe branch. Placed in a sealing manner against the two open end faces of the inserted starting piece of pipe in each case is a plunger which is movable in the forming tool and can be pushed axially into the forming took in each case by a pressure cylinder. The interior of the starting piece of pipe is filled with pressure fluid by means of an opening in at least one of the plungers, prior to being placed on the plungers in a sealing manner. A fluid high-pressure is built up by pushing the plungers axially into the forming tool with high force and, thus initiated, by pushing pipe wall material axially towards the forming point, the pipe wall material is pressed into the cutout in the forming tool and the T-shaped branch is thus shaped. In order to be able to manufacture T-pieces with a curved branch, the end face of the T-shaped cutout for the pipe branch is supported with controllable force by means of a flexible mandrel.