Abstract: A wedge anchorage for an axially elongated tension member, encased in and arranged to prestress a concrete structure, includes an anchor member with a conically widening surface where a wedge seats for securing the tension member in the tensioned state with a cap arranged to fit in locked engagement with the end of the anchor member through which the tension member extends out of the concrete structure. The cap has a cover wall extending transversely of the axial direction and spaced from the anchor member. An opening is provided in the cover wall through which the tension member extends out of the concrete structure. A spring or other biasing member is located within the cap for limiting axial displacement of the wedge when the tension member is stressed in tension. This arrangement avoids the formation of a recess in the surface of the concrete structure from which the tension member extends and the need for a filler member for sealing off the recess when the prestressing operation is completed.