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Magnetomechanical damping measurements are commonly made using wire specimens in a torsion pendulum. Twisting the cylindrical wires produces tensile stresses along a helix. An analytical study was made relating the direction of these stresses with the directions of the crystallographic axes assuming three different orientations of the crystal, 〈100〉, 〈110〉, and 〈111〉, along the axis of the wire. The results make it possible to calculate the correct magnetostriction values to be used in the mathematical model of magnetomechanical damping when there is preferred orientation in the specimens. Magnetostriction values are calculated over the temperature range of 78° to 300° K for iron, nickel, and an iron‐3.8% silicon alloy and these are compared with the magnetomechanical damping maxima in the same temperature range.