A tape-shaped Ti–Ni shape memory alloy (SMA) element, which demonstrates superelastic behavior, shows negative stiffness during post-buckling deformation. This characteristic is applied to a passive vibration-free system using a zero-stiffness structure. However, the post-buckling behavior (negative stiffness) of an SMA element can be varied by modifying its dimensions. In this study, the effect of the thickness of a tape-shaped SMA element on its post-buckling behavior is investigated by finite element method (FEM) analysis. The magnitude of the negative stiffness increases with the thickness. Furthermore, the rate of increase of the volume fraction of the martensitic phase before the start of buckling deformation increases with the thickness. From these results, we conclude that the magnitude of negative stiffness during the post-buckling of a tape-shaped SMA element depends on the variation of the volume fraction of the martensitic phase during buckling deformation.