The analysis of oil seals is of great concern for the proper design of high pressure centrifugal compressors, because they can have significant influence on the dynamic stability of the compressor rotor. The lack of adequate analytical tools highlight the need for this type of study. An analytical tool to evaluate the oil seal characteristics, perform linear stability analysis of the compressor rotor and nonlinear transient analysis of the compressor rotor and the seal ring has been developed. An iterative finite element method is used to solve the non-linear and coupled hydrodynamic and thermal equations for the pressure and temperature distributions in oil seals. The perturbation technique is employed to determine the static and dynamic characteristics of oil seals. The hydrodynamic forces are calculated by integrating the pressure distribution along and around the oil seal. Eigenvalue analysis is performed to do the linear stability analysis of the compressor rotor. A numerical integration technique is used to solve the non-linear equations of motion of the seal ring and compressor rotor. This analysis has the ability to handle tapered seals, circumferentially grooved seals and seals with shaft misalignment. Results obtained from linear stability analysis and non-linear transient analysis for different seal geometries, including shaft misalignment, are presented. For centered seals, results obtained are in good agreement with a previous finite difference analysis. At an operating eccentricity of 0.098, the maximum percentage differences in the cross-coupled stiffness and direct damping coefficients obtained from this analysis and the finite difference analysis are 5.1 % and 1.5 % respectively. For eccentric seals, use of the true temperature distribution gives significantly different results. At an operating eccentricity of 0.497, the maximum percentage differences in the cross-coupled stiffness and direct damping coefficients obtained from this analysis and the finite difference analysis are 17.7 % and 22.9 % respectively. This analysis shows that the sharp edge grooves decrease the axial flow rate. In addition, groove depth typically applied to industrial seals is shown to be effective in breaking up the hydrodynamic pressures. Tapered and circumstantially grooved seals are shown to enhance both the locking mechanism in the seal ring and the dynamic stability of the compressor rotor. The resulting computer program gives the designer of compressors with liquid seals a much needed capability that is not available from any other known source. / Ph. D.