The concept of a bistable structure as an energy absorbing structure is presented. A bistable structure is capable of distributing damage throughout the whole body, thus increasing the amount of energy dissipation. Using this concept, a helicoidal bistable structure is developed. We investigate a structure in which a helicoidal orthotropic shell envelops a solid cylinder. The center core of the structure is treated as a linear-elastic isotropic material. Numerical simulations of damage (breakages) are performed under static loads, and the force-displacement relation is obtained as a result. As an energy absorbing structure, the helicoidal bistable structure can absorb more energy than a conventional structure before it fails. The helicoidal bistable structure can be designed to sustain a small elongation while still being able to release energy effectively. The additional twisting degrees of freedom correspond to the additional energy released in the process of elongation.