The rotation of a deforming body is usually evaluated using the antisymmetric tensor W (W-spin) constructed from displacement incremental gradient tensor L. On the analysis (Nagtegaal and de Jong, 1982) in which W-spin was applied to the torsion test of a circular tube, the phenomenon appeared where the stress was oscillating. Various studies have been made to find out the cause of the oscillating, but it hasn’t yet been obtained sufficiently. In-plane rotation of a line element on a coordinate plane depends on its orientation. The W-spin represents the average value of the rotation, but does not always correspond to the in-plane rotation of the coordinate axes. Then, taking place of W-spin, in this paper we used pseudo spin which takes especially the in-plane rotation of coordinate axes into consideration, and applied to the torsion test. The oscillating of the stress value was completely disappeared.