Stability of the annular recess conical hydrostatic thrust bearing supporting a rotor is studied. The one dimensional Reynolds equation with rotational lubricant inertia term is analytically solved to obtain the pressure distribution under dynamic conditions. After linearising the dynamic force, equation of dynamic equilibrium for the upper pad of the bearing with rotor mass is written and the time constants are evaluated. The influence of bearing aspect ratios, resistance ratios, mode of compensation (capillary and orifice), cone angles and rotation on the stability of the system are studied.