We derive the shape equations in terms of Euler angles for an uniform elastic rod with isotropic bending rigidity and spontaneous curvature and spontaneous twist rate. We study the elasticity and stability of a helical filament under uniaxial force. We find that there is no sharp transition for the extention of a helix when using supercoiling degree as an independent variable. This result suggests that the elastic response of a helical filament using the supercoiling degree as independent variable must be quite different from using the torque as independent variable. We also find that a large negative supercoiling degree tends to destabilize the helical filament.