The behavior of a buckled beam mechanism, which exhibits both bistability and negative stiffness, is investigated for the purposes of passive shock and vibration isolation. The vibration and shock isolation systems investigated in this research include linear, positive stiffness springs in parallel with the transverse motion of buckled beams, resulting in quasizero stiffness behavior. For vibration isolation systems, quasizero stiffness lowers the resonance frequency of the system, thereby reducing its transmissibility at frequencies greater than resonance. For shock isolation systems, quasizero stiffness provides constant-force shock isolation at tailored force levels, thereby enabling increased capacity for absorbing shock energy relative to a comparable positive stiffness system. Single- and double-beam configurations that exhibit first-mode buckling are utilized for vibration isolation, and a single beam that exhibits first- and third-mode buckling is used for shock isolation. For all cases, the static and dynamic behavior of each configuration is modeled analytically. The models are then used to design prototype vibration and shock isolation systems that are fabricated using selective laser sintering (SLS). The dynamic behavior of the systems in response to base excitations is determined experimentally, and the results are compared to model-based predictions. The vibration isolation prototypes display isolation levels that are tunable by varying the axial compression of the beams. Double-beam systems are shown to provide greater reductions in resonance frequency than single-beam systems for comparable levels of axial compression. However, low-frequency isolation capabilities are sensitive to the high levels of precision required to obtain low levels of system stiffness. The shock isolation prototype provides isolation at prespecified threshold levels of force or acceleration. In the prototype system, an input shock with a peak acceleration of approximately 7 g is reduced to a peak acceleration of the isolated mass of approximately 1 g. High levels of negative acceleration are observed in models and prototype systems when the buckled beam snaps back to its original position; however, models indicate that large negative accelerations can be mitigated using one-way dampers.