Abstract: In a built-up core for the bead of a pneumatic tire, the wires (A,B,C) of each lay (8) of the built-up core (4) are of a trapezoidal cross section. Between the wires (A,B,C) of each lay (8) of wire and the wires (A,B,C) of the next, overlying lay (8) of wire, there are wedge-shaped clearances (9). As a result, the wires (A,B,C) of each lay (8) of wire find a support on the edges of the wire of the underlying lay of wires so that they cannot be displaced against each other during the production of the tire.