In this paper we present measurements of the field dependence of Young's modulus E(H) and shear modulus G(H) for amorphous wires of composition Fe77.5B15Si7.5. E(H) was measured by a vibrating reed method and G(H) by means of a torsional pendulum. For as-cast wire the maximum change in either modulus is about 2%, and the form of the field dependence is consistent with the rotation of moments in the outer sheath from a radial to an axial direction, analogous to the moment rotation model for transversely field annealed ribbons. The small magnitude of the modulus changes is a consequence of the rather high anisotropy of a few kJ/m3 associated with the casting stress. The modulus changes in current annealed wires are much greater than in the as-cast state, with ratios E(min)/E(max) approaching the largest values found in transversely field annealed ribbons. This is consistent with the reduction of the radial stress by annealing, but also indicates the retention of a substantial proportion of off-axis moments. The significance of these results in the light of present understanding of domain structure in amorphous wires is discussed.