An accidental collision with bridge structures can have catastrophic consequences. Such collisions have resulted in human casualties and partial or full collapse of bridge structures. In the U.S., 15% of bridge failures were due to a vehicle collision. Increasing traffic volume resulted in an increase of collision events, especially with over-height trucks on highways. Innovative impact protection systems have become a point of interest to protect both structures and human lives. Metamaterial systems that have the ability to exhibit unusual properties such as negative stiffness behavior can dissipate high levels of energy. Such systems became a point of interest in base isolation, impact protection, and shock absorption applications. Bi-stable elements such as pre-buckled beams can be designed to exhibit negative stiffness behavior under transverse loading. Recent studies have shown that such systems can dissipate up to 70% of the input energy by transferring from one mode of buckling to another. The snap-through behavior of such elements remains in the elastic region of the material, which allows the system to recover the initial configuration after unloading. Finite element modeling (FEM) of bi-stable elements was carried out to address the bi-stability behavior and predict the force threshold as well as the amount of energy dissipated through such elements. FEM results were validated with experimental results. Key parameters that affect the behavior of bi-stable elements were investigated to study the different force thresholds and energy dissipation levels. The developed FEM can be used to predict the behavior of bi-stable elements and hence, design them in accordance with force thresholds and energy dissipation requirements.