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Stability analysis of high-speed machinery based on rigid rotor model mounted on rigid supports was found to be inadequate for stability predictions. But in actual practise bearings have some flexibility. Stiffness and damping properties of fluid film bearings alter the critical speeds of a rotor. Dynamic coefficients of fluid film bearing are dependent on speed, geometry of the bearing and other operating conditions. Plain circular bearings do not suit the stability requirements of high-speed machines and precision machine tools. Alternate bearing designs are sought to meet the new requirements. But a very little information is available in this field. In this work dynamic characteristics and stability of rotor-bearing system supported on circular and non-circular hydrodynamic bearings (short bearing and finite bearing) is studied. To demonstrate the worth of the study, it is proposed to take up models like bearings supporting rigid rotor and simplified flexible rotors for different bearing configurations. This study appears to provide a better understanding of this type of problem and the present results should be utmost importance to rotor-bearing system designers and analyst.