Passive vibration isolation is a key element to achieve precise results in milling processes and to increase tool durability. Damping of vibrations near to the cutting edge is considered highly effective as well as hard to implement because of the limited damping properties of conventional materials in the available space. The use of damping elements made of NiTi shape memory alloys (SMA) represents an innovative approach. Their use is based on the ability to convert mechanical energy into thermal energy through the pseudoelastic effect, whereby the pronounced conversion hysteresis of the material provides information about the usable damping potential. Studies on the properties of pseudoelastic SMA under compressive loading are only sporadically available in comparison to tensile loading. In this paper, the stress-compression curves and the hysteresis energy of tests results are compared with the results of finite element simulations. The simulation results based on the material model used so far is a good basis for the further development of damping elements.