This dataset belongs to the article "Buckling Metamaterials for Extreme Vibration Damping". This dataset can be used to reproduce all data reported in this article. Abstract Damping mechanical resonances is a formidable challenge in an increasing number of applications. Many of the passive damping methods rely on using low stiffness dissipative elements, complex mechanical structures or electrical systems, while active vibration damping systems typically add an additional layer of complexity. However, in many cases, the reduced stiffness or additional complexity and mass render these vibration damping methods unfeasible. Here, we introduce a method for passive vibration damping by allowing buckling of the primary load path, which sets an upper limit for vibration transmission: the transmitted acceleration saturates at a maximum value, no matter what the input acceleration is. This nonlinear mechanism leads to an extreme damping coefficient tan delta ~0.23 in our metal metamaterial|orders of magnitude larger than the linear damping of traditional lightweight structural materials. We demonstrate this principle experimentally and numerically in free-standing rubber and metal mechanical metamaterials over a range of accelerations, and show that bi-directional buckling can further improve its performance. Buckling metamaterials pave the way towards extreme vibration damping without mass or stiffness penalty, and as such could be applicable in a multitude of high-tech applications, including aerospace structures, vehicles and sensitive instruments.