The author's theory of elasticity of the second order is being applied to calculate the increase of torsional stiffness of a prismatical bar when an axial tension is initially imposed upon it. It is found that the classical shear stress distribution is not affected by the axial stress. However, an increase of torsional stiffness is produced due to the fact that the boundary condition over the cross section contains not only the shearing stress but also the product of the axial stress by the rotations. This increase of torsional stiffness turns out to be proportional to the polar moment of inertia of the cross section with respect to its center of gravity.