Cone disc springs exhibit quasi-zero stiffness behavior that is useful in isolating objects from low frequency vibrations. However, the stroke of a single disc spring is too low for most applications, and springs are stacked to increase the displacement. A method to contain the isolator stack then becomes critical for practical uses. Many challenges in developing these containment methods have been identified and can be collectively described as how to appropriately contain the stack without affecting isolation performance. In this work, three designs are considered: a retaining ring design, tube and shaft design, and zero poisson ratio sleeve design. Disc spring stacks with containment method are built, and load-deflection curves are measured and compared with standalone stacks. Under quasi-static compression testing, each containment method has minimal effect on the standalone stack load-deflection curve. However, significant differences in isolation performance are observed in vibration testing and found to depend on characteristics such as lateral stability, lateral strength, and degrees of freedom. Lastly, advantages, disadvantages, and appropriate applications for each containment method are summarized. The conclusions of this work are that containment method is an important variable in the application of disc spring isolators and robust, versatile containment designs have been demonstrated.