We have found that transverse field annealed ribbons of Metglas 2605 SC exhibit shear modulus variations, &Dgr;&mgr; effect, larger than 50 and transverse coupling coefficient about 0.99. Excited in standing torsional wave the peak resonant frequency has been measured as a function of the applied tensile stress when a constant dc current was flowing through the ribbon. A simplified model has been developed in order to explain the appearance of such giant values, one order of magnitude larger than any other previously reported. It has been found that the symmetrical distribution of shear strain concerning the longitudinal and transverse ribbon axes is the main source of the magnetoelastic effects enhancement.