Determination of Joule magnetostriction by the method of tensile strain measurement has a lower limit of about 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-6</sup> because of error strains clue to magnetostatic forces and changes in temperature. It is shown that these disturbances can be eliminated by measuring shear strains induced in thin-walled tubes by helical magnetic fields. By a resonance method, the measurement of the magnetostriction constant can be made down to 10 <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">-13</sup> .