In treating film lubrication, Reynolds and Sommerfeld confined themselves to surfaces of infinite width, for mathematical reasons. Michell obtained the solution for a plane surface of finite width; the importance of this lies in the fact that leakage of lubricant through the lateral edges of a finite bearing reduces considerably the load supportable by the bearing. Solutions are obtained here for general cases of rectangular bearings with surfaces curved in both directions; for the Michell sector type of thrust bearing plate, in a case which allows consideration of the effect of the variation of film thickness with the radial distance from the center of rotation; and for the fitted finite journal bearing. General methods are exhibited suitable for handling other cases. In particular, the equations for the finite journal bearing in the general case are partially developed. Solutions for the journal bearing are shown to require laborious computation, so that an approximation to the film thickness is preferable; such an approximation, which can be handled relatively easily, is treated, and the solution obtained.