An entirely new theoretical concept of hydrodynamic instability, oil whirl, is presented. Starting from Reynolds Equation and employing the short bearing approximation due to Ocvirk the equations of motion of a journal on an oil film are deduced. Only plain journal bearings and rigid shafts are considered but an out-of-balance force is included. Instead of linearization of the system, as in every previous investigation, all the non-linear terms are retained. The complex equations are solved on an analogue computer and produce some notable results. Non-linear modes of vibration occur which have the characteristic frequency of,whirl, namely half that of rotation. This is an important discovery and shows the inadequacy of linear stability theory. Also the frequency changing properties of an oil film are demonstrated and some of the apparent contradictions of previous experimental work explained. An attempt is made to establish the non-linear theory in practice and to investigate the effects of imperfections in the geometry of the shaft or bearing. it is evident from earlier work that misalignment, ovality, etc. have an appreciable influence on the occurrence of whirl. A large clearance bearing based on Dr. Cameron's idea is used for it is particularly suitable to these studies. .However the thick oil film of the model approach is found to produce undesirable distortions of the oil film forces. The main cause is the high oil inertia, an effect which is normally negligible. Even so it is found that its influence can be beneficial in preventing whirl.