A study is made on the parametric stability of open thin-walled beams under axial load. A set of nonlinear equations of stability and the appropriate boundary conditions are obtained using the energy approach. The derived equations are applicable to thin-walled open section of any shape. The effect of longitudinal deformation is taken into account in the derived theory. Using the nonlinear theory, the torsional parametric stability of a beam of a symmetrical 1 section is studied. The principal region of torsional instability is determined. The steady-state amplitude of torsional oscillation when the system is parametrically excited is found. Finally, the transient growth of the torsional motion from the onset of instability to the steady-state oscillation is computed. The effect of viscous damping on the steady-state and transient response is also included in the analysis.