A torsional pendulum has been built using a stress relieved FeSiB amorphous wire. Torsional motion is magnetoelastically induced by means of the simultaneous application of longitudinalHzand circularH&fgr;magnetic fields. The experimental setup allows one to determine both the torsional deformation and the changes in the longitudinal magnetizationMzof the wire. Free and forced oscillations are observed depending on the parameters of the applied fields. In both forced and free oscillation modes two resonant peaks are observed. Their frequency and amplitude dependences on the axialHzand circular fieldsH&fgr;have been studied. Changes in shear modulus &Dgr;Gvalued 60% in excess have been measured. To interpret the experimental results a theoretical model is developed taking into account the existence of two different magnetic regions in the wire, core, and shell having a different distribution of axial, radial, and shear stresses. The calculations explain the more remarkable aspects of the observed behavior. ©1995 American Institute of Physics.