The field dependence of Young's modulus (Delta E effect) of amorphous wires of Co72.5Si12.5B15 has been studied in the as-quenched state, and after annealing for times between one and several hundred minutes at temperatures of 450, 480, and 500 degrees C. In the as-quenched state the Delta E effect is small (<2%), because the quenching stresses couple with the magnetostriction (lambda(s) similar to-3X10(-6)) to produce significant anisotropy. Annealing for short times (>1 min) is sufficient to relieve much of the quenching stress, resulting in magnetic softening and enhanced Delta E effect (at best >30%). Further annealing eventually reverses these trends, increasing coercivity and anisotropy, and reducing the Delta E effect. This behavior is attributed to surface crystallization. The results are interpreted in terms of the core-shell domain model, and are consistent with the retention of a significant component of circumferential domain structure in the shell in all annealing conditions studied. (C) 1996 American Institute of Physics.