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 longitudinal Hz and circular Hφ magnetic fields. The experimental setup allows one to determine both the torsional deformation and the changes in the longitudinal magnetization Mz of 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 axial Hz and circular fields Hφ have been studied. Changes in shear modulus ΔG valued 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.