In the construction of a prestressed concrete structure, such as a bridge girder, forms for at least a part of the structure are built and a thin-walled sheathing tube is placed within the forms. Axially displaceable stiffener tubes extend through the sheathing tube. After the concrete is poured into the forms around the sheathing tube and sets, a steel bar is pushed through the sheathing tube and displaces the stiffener tubes. The steel bar can be left in the sheathing tube as the tendon or replaced with a tendon. Subsequently, the tendon is tensioned. Spacers encircling the steel bar keep it centered as it is pushed through the sheathing tube. Preferably, the stiffener tubes consist of an inner tube and an outer tube and each is made up of a plurality of short axially extending lengths with the joints of the inner tube staggered relative to the joints of the outer tube.