The driving speeds at which self-excited motions occur in rotor-bearing systems are commonly referred to as "instability threshold". These speeds and the magnitude of rotor (journal) trajectories are two important variables characterising the limits and states of a rotating machinery. The hydrodynamic lubrication in journal-bearing provides damping and reduces friction on rotor systems; therefore the journal amplitude should not exceed the bearing radial clearance. Linear bearing models are not able to accurately predict the journal trajectories for rotor-bearing system operating in conditions where the system does not have period one solutions, or when the journal motion is larger than 20-30% of the bearing radial clearance. Therefore the nonlinear bearing impedance descriptions method was used to model the hydrodynamic reaction forces. Two cases were analysed: 1) a rigid non-symmetric rotor and 2) a flexible non-symmetric rotor. The two models consist of a rotor supported by two identical finite-length hydrodynamic journal bearings of length to diameter ratio L/D=1, with same lubricant properties. The flexible non-symmetric rotor was modelled by the finite element method (FEM). Simulation results show that the instability threshold of the rigid non-symmetric rotor-bearing system (case1) depends on the low stability characteristics of the less loaded bearing. But when the shaft flexibility and the gyroscopic coupling effect are taken into account; the instability threshold increases for the flexible non-symmetric rotor-bearing system (case2). The gyroscopic coupling effect does not only increase the instability threshold, but the journal trajectories magnitude has also significantly increased. This is normally not a preferable condition since high vibrations will induce heat and stress in babbited bearing.