The aim of the work reported in this thesis was to develop a method, suitable for general design work, to determine the stability of a simple rotor mounted in hydrodynamic bearings, The rotor model used was a simple spring mass system, but the bearing model allowed a comprehensive range of bearing cross-sectional shapes and grooves to be assessed. The oil film equations were solved by the successive over-relaxation finite difference technique. The problem was approached by considering the energy balance of the bearing-rotor system. The hydrodynamic oil pressure film in the bearing performs work on the journal and this is largely responsible for the decay or growth of the rotor motion. The behaviour of a simple rotor was investigated to determine if its influence on the bearing could be represented by a simple force locus as this would allow the oil film work to be calculated without marching out the rotor locus. In general, the force exerted by the rotor on the journal is too complex to allow a direct assessment of the stability of a system by this technique. The flexibility and ease of operation of the directly loaded bearing computer program make it useful for comparisons of bearing design features and load conditions. An investigation was carried out into the effect of the bearing parameters on the oil film work when the journal is loaded with a circular force locus. An attempt was made to reduce the computation necessary to march out the journal and rotor loci. The approach taken was to improve the utilisation of the information obtained from the oil film equations. Although significant reductions in the computation were achieved, they were insufficient to justify the additional program complexity.