A vibration analysis of a high-speed rotor-bearing system using the finite element is presented. Models were developed to study the effect of rotor mass and stiffness, support bearing stiffness, and bearing pedestal stiffness on rotor critical speeds. Bearing stiffnesses were obtained from a previously-developed computer program. Pedestal stiffnesses were obtained from a plane-stress finite element analysis. A rotor model which incorporated these bearing and pedestal stiffnesses was then analyzed using a three-dimensional finite element analysis to determine its critical speeds. Results of this analysis are compared to experimentally obtained data and discussed. Recommendations for future analyses, experimental developments, and rotor configurations are given. / Master of Science