In the high stiffness hydrostatic thrust bearing in which the land supported elastically could displace instead of shaft movement against load fluctuation, a new elastic supporting construction without friction while land displacement is proposed. With regard to the static performance, this bearing shows infinite stiffness within the load carrying capacity of 0.4 to 0.9 under the optimum condition and this agrees well with the calculated results. Meanwhile, the self-excited vibration takes place sometimes in this bearing for the lowering of damping capacity. The stable region for the vibration is examined and the factors which influence it are clarified. Then in order to suppress the self-excited vibration, a squeeze film damper which does not affect the static performance is installed inside the bearing body. By this damper, stable operation under the optimum condition becomes possible with the proper matching of the squeeze clearance and oil viscosity or oil temperature. The effect of the damper is also confirmed by the stability analysis.