The magnetomechanical effect and the magnetostriction in the -oriented single crystal of Fe0.81Ga0.19 alloy have been investigated on the basis of Stoner-Wohlfarth model. The results have shown that in the demagnetized state the degeneracy of the resultant anisotropy in the alloy from the original cubic magnetocrystalline anisotropy into the biaxial anisotropy occurs under a critical stress. This leads to an increase in the fractional occupancy of 90° domain which causes an increase the bulk magnetostriction.