An experimental study of the effect of axial tension on the torsional stiffness of circular wires was made under static conditions and well within the elastic limits for both twist and stretch. The method used was to apply a constant couple to the bottom of a vertical wire and to note optically how the angle of twist changed as the tension on the wire was varied. It was carried out with four different alloys. Variations in angle were observed to be related linearly to the applied tensions and to be in excess of those which arise from the change in dimensions, except for one alloy for which the effect is either nonexistent or too small to be detected. In all cases there is an initial residual twist. In general, an increase in axial tension produces a decrease in torsional stiffness, except where the effect of the residual twist is greater than and opposed to this decrease. The results are also shown to be in qualitative agreement with the classical experiments on the Poynting effect, an effect which can be explained by modern second‐order theory of elasticity.