This thesis is concerned with the development of a nunerical technique for the computational analysis of ruptured liquid films in both steadily and dynamically loaded bearings. The approach is based on the principle of oil flow continuity. A cavitation algorithm, proposed by H. G. Elrod, was implemented for studies of hydrodynamic lubrication in infinitely long cylinder/plane bearings (i.e. non-conformal contacts) under combined sliding, rolling and normal motion. Difficulties involved in the implementation of this algorithm were investigated in great depth. A new 'improved' method of solution, which is well-suited to the computational analyses of steadily and dynamically loaded bearings, was developed. The improved technique involves the solution of the hydrodynamic lubrication problem for oil film pressures or degrees of lubricant filling in the full film and cavitated regions of a bearing. Detailed studies of cylinder/plane under conditions of both instantaneous and sinusoidal normal motion were performed. The improved solution was shown to facilitate the implicit implementation of the Jakobsson-Floberg-011son boundary conditions (i.e. the inclusion of 'oil film history' phencinena) in dynamically loaded bearing analyses. Detailed comparisons between the oil film history and classical solutions, and published experimental studies were made. Computer programs based on the classical Reynolds equation and the improved method of solution were developed for the analysis of circuTiferentially grooved, finite journal bearings operating under steady-state and dynamic loading conditions. The improved method of solution produced more realistic predictions of performance characteristics, particularly oil film extent, oil flow and bearing power loss. Comprehensive comparisons with published theoretical and experimental studies were made. Encouraging agrenent was obtained between the oil flow continuity analyses and experiments. Journal centre orbit analyses of dynamically loaded bearings, typically found in reciprocating engines, indicated that the oil film history solution may reveal a nunber of new features of time-varying performance characteristics not previously predicted by the classical Reynolds solution.