In this paper a numerical investigation relative to the static behaviour of thin-walled beams of open cross-section, undergoing moderate angles of twist, is presented. The constitutive equations between nominal stresses and Green strains are assumed to be linear elastic and isotropic. The numerical results are obtained by using a finite element approach, following a classical Newton-Raphson procedure. They show the peculiarity of the non-linear dependence of the torsional torque on the corresponding angle of rotation, which can be either of hardening or softening type. Comparisons with previous numerical results available in literature are also provided.