A tooling for manufacturing by stamping parts made of thermoplastic material from a blank of the material. A hollow die is delimited by a bottom, side walls and an opening opposite the bottom, and a raised punch designed to cooperate with the die via the opening. The tooling includes at least one mobile element to cooperate with at least one recess placed in the bottom and/or side walls of the die, the recess allowing the passage of one part of the blank that is to be bent using the mobile element.