Superelasticity behavior of helices has been the focus of recent research in micro-/nano-engineering, while the traditional Kirchhoff rod model restricts itself in the bending and torsion conditions. With the aid of the concept of a Cosserat curve, a novel theoretical basis has been established for statics and dynamics of helices with essential extension and shear, which is able to quantitatively analyze the superelastic mechanical properties. Except for a good agreement with the experimental observation, numerical solutions have shown that we cannot only predict two important properties of the superelasticity characteristics: the breaking force and the stretch of the coil wire under the axial loading, but also precisely describe and explain the Hooke’s constant and torque in the entire stretching and breaking processes. The present work has provided useful information for the future experimental investigation on superelasticity as well as its application in meta-/quantum devices.