A theoretical analysis is presented investigating the stability (fractional frequency whirl, “oil whip”) of a symmetrical, flexible rotor supported in journal bearings. The bearings are mounted in flexible, damped supports. The analysis determines the rotor speed at which instability sets in as affected by rotor stiffness, the dynamic properties of the bearing film, and the flexibility and damping of the bearing supports. The analysis is based on the fact that the bearing can be represented by frequency-dependent spring and damping coefficients, and the method by which the coefficients are obtained is described with emphasis on the gas-lubricated bearing. The conclusions are: (a) Rotor and support flexibility by themselves lower the speed at onset of instability; (b) when the bearing support possesses damping in addition to flexibility, the speed at onset of instability can be raised significantly above the threshold speed of a rotor in rigidly mounted bearings. Numerical results are presented in the form of graphs for the plain cylindrical gas bearing.