This paper describes an analytical technique to calculate the damped critical speeds and the instability threshold speed of multimass rotor-bearing systems. Necessary equations are developed to study the effect of bearing as well as bearing support flexibility and damping on the system stability, thereby enhancing the current state of the art. Included in the analysis are the effects of linearized disk gyroscopic moments, shear deformation, and speed dependent bearing characteristics. The method of solution is based on the Transfer Matrix approach and uses complex variable notation to develop the overall system matrix. Mutter’s quadratic interpolation technique is employed to extract the complex eigenvalues of the rotor system and the corresponding mode shapes are found by back substitution. The analysis has been programmed for digital computer solution. Computational time is saved by eliminating from the polynomial the complex conjugates of the roots already found. Numerical overflow/underflow is controlled via scale factors. In addition to calculating the damped critical speeds, the computer program also provides information about the undamped frequencies, peak response frequencies, response amplification factors, and logarithmic decrements of the system. The accuracy of the predictions of the program has been verified and is shown to be acceptable for typical rotor systems. The results of an extensive investigation of an intershaft journal bearing instability in a dual rotor system are summarized. The stability map for this system is presented and clearly indicates the effect of rotor radial misalignment on system stability.